So they not only start with Batman's origin story, they have to make it a weird mishmash of flashback and fantastic dream, just to get the whole movie off on a WTF? note.
_Then_ they go to Bruce Wayne rushing into Metropolis on the day Superman and Zod had their throw down in Man of Steel. Here's there because he owns a building in Metropolis and he's worried about the people in there. He's especially worried about some manager there, but we really have no idea who he is or why Bruce cares about him so much, which makes it kind of hard for us to care about him. Of course he gets killed, and lots of other people get killed, and some people get maimed.
This is supposed to be the starting point for Batman's desire to take down Superman. But it's not very well articulated. His journey from "maybe we should be concerned about Superman" to "maybe we should do something about Superman" to "let's kill the fucker" doesn't seem to have the clearest motivation. It seems like we're supposed to believe he was manipulated into it, but the evidence of that manipulation is pretty scarce. One of Batman's defining characteristics is supposed to be his intelligence, but he doesn't seem to be demonstrating a lot of it in this regards. One of Batman's other defining characteristics is that he's frequently considered to be at least a little mentally unbalanced, but he doesn't seem to be crazy enough in this to fall into the anti-Superman paranoia without asking more questions than he does.
The biggest factor in favor of the slide into madness is the dream sequences. You know all those scenes in the trailers of Superman being a total asshole, accepting homage from fascist-looking soldiers and such? All the things meant to make you think that maybe Batman wasn't a total loon for wanting to fight Superman? Surprise! Those were all figments of Batman's imagination!
Or maybe not! Because there are hints that maybe they're prophetic? After one dream he sees some kind of rift in space and/or time and someone that may be the Flash or might be someone else who maybe came back in time to warn Batman about maybe Superman or maybe someone else. But that also turns out to be a dream... maybe?
Or since we learn later that Lex Luthor has (probably?) been setting up the confrontation between Batman and Superman then maybe Lex Luthor somehow caused those dreams? But if so then there's no explanation at all about how he might have done so. However if Lex _was_ pushing Batman towards fighting Superman he either knew that Batman was suffering weird dreams about him (if he wasn't causing them himself) or he thought that Batman was much more manipulatable than he actually was.
Meanwhile Batman spends a lot of time trying to hunt down information about the "White Portuguese", which he thinks is a person and he wants to discover for... reasons that aren't really explained? He's apparently lied to Alfred about why he wants to find "him", but we're not told what the excuse is, so it's all kind of weird and confusing. Then he discovers it's a ship, which is apparently a big surprise to him but kind of an "okay whatever" from the audience since we had no real idea what he was expecting to find in the first place.
So while this is going on Superman is getting framed for murder. Lois Lane is tricked into going into a terrorist military camp to interview their leader. But she's being used by the CIA, who (maybe?) planted a tracker in her cameraman's camera (the cameraman happens to by Jimmy Olson, but we're never told that in the movie) which is discovered by some of the terrorists who are actually mercenaries who were secretly inserted into the camp by, we later find out, Lex Luthor.
The terrorist leader takes her into a building, where she attempts to convince them that she didn't know about the tracker, and as soon as they're gone the mercenaries kill everyone else. Both the terrorists and the rest of the news crew, including Jimmy Olson.
Superman shows up and rescues Lois Lane, presumably killing the terrorist leader in the process, and then gets blamed for the murder of everyone else in the camp. Because either forensics thinks being shot by automatic weapons is indistinguishable from being punched by Superman, or they figured Superman was running around with an AK-47.
So Lex Luthor has decided that the world needs a deterrent against Superman, or at least that's what he's claiming when he asks the US Government to let him import some Kryptonite from the second alien crash site (the big terraforming thing that Superman destroyed in the... Indian Ocean?) But clearly he actually wants to kill Superman, except it's never made clear exactly why.
The government decides that making weapons that could kill Superman is a bad idea, so Lex Luthor smuggles the kryptonite in on a ship named.. the White Portuguese! So since Batman also wants to murder Superman at this point he tries to steal the kryptonite, and in the process murders a lot of other people. But he's inadvertently stopped by Superman, who's there to tell Batman to stop being Batman and murdering people.
I am very unsure at this point about whether Lex Luthor actually expected/wanted Batman to steal the kryptonite at that point. He looks perplexed when the kryptonite shows up at his lab, but i couldn't tell if that was because he wasn't expecting it to arrive, or just because the convoy had been decimated by Batman before Superman intervened.
As the film progresses Lex starts acting more and more unhinged, and again it's not clear why this is happening. Was he always unhinged and just doing a better job of covering it up before? Or is he gradually going insane over the course of the film? I can't say.
He manages to blow up a Senate hearing that was going to conduct an investigation of Superman's actions... but i'm not sure why. If he intended to frame Superman for the explosions it was a total failure. Apparently some people (including Superman himself) wondered why he didn't or wasn't able to stop the explosion, but no one blamed him for causing it. The panel was headed by the Senator who refused to give him the import license for the kryptonite he wanted, but if it was intended as revenge for that slight it seemed rather... petty. Especially since he had no trouble getting the kryptonite anyways. (In fact given that Batman was searching for the White Portuguese from practically the start of the movie implies that that was Lex's real plan all along.) If it was just intended to rattle Superman it seems to have been ineffective.
So Superman goes on walkabout (again) and has a dream vision of his dead dad.
Batman breaks into Lex Luthor's labs and steals the kryptonite (Is Lex surprised? Thankful that his plans are back on track? I have no idea) and makes a bunch of weapons out of it. Mainly gas grenades and a spear.
Meanwhile Lex has convinced the military to give him Zod's body and access to the first crashed alien ship (still sitting in the middle of Metropolis.) He slices off Zod's fingertips so he can access the ship's systems. How did he know that would work? I have no idea. He then accesses the library in the biolab. How did he know he could do that? I have no idea. He then uses the biolab to combine his blood with Zod's body to create a giant kryptonian monster. How did he know he could do that? I have no idea. You could say he learned it from accessing the library, but if so then it's _very_ coincidental that he learned from the library that he could use the body he already had to create the tool he needed as the culmination of the plot that he'd already put in motion before the start of the movie.
So then he kidnaps Martha Kent and Lois Lane. He drops Lois Lane off of a tower so that Superman will come rescue her. Where was Superman when Lois Lane was dropped? Last we saw him he was in some mountains, presumably hundreds or thousands of miles away. Yet somehow he heard her screaming at the point she was first dropped of the building and was able to get there before she hit the bottom. Or perhaps he was already back in the city and was just being really lax about Lois Lane getting kidnapped up until that point. Whatever.
So when Superman confronts Lex he shows them that he has Martha captive, and will kill her in an hour unless Superman fights Batman.
So Superman flies over to Batman who VERY COINCIDENTALLY had decided that was the night to challenge Superman, by lighting up the Bat Signal and waiting. (I'm 80% certain Lex had already started his *ahem* Doomsday plan before Batman lit the signal, so i don't think this was cause and effect.)
Superman then makes half an attempt to explain to Batman what's going on. Batman interrupts him and Superman then decides that any further attempts at explanation are useless until they've fought. Superman doesn't actually want to kill Batman of course, so he drags the fight out until Batman is able to bring his kryptonite gas grenades into play an even the odds.
Once Superman starts losing the fight he _still_ doesn't make any attempt to explain what was going on.
Finally, when he's pinned to the ground and about to be stabbed by the kryptonite spear, he gasps out something along the lines of "save Martha."
SHOCK! THAT IS THE SAME NAME AS BRUCE WAYNE'S MOM!
Batman goes "what?" and Superman says something more about Martha needing to be saved.
Now Batman, the guy who at this point has been insanely fixated on killing Superman for no really good reason except his somewhat psychotic dreams suddenly goes "well our mom's had/have the same name, i guess that's a good enough reason to be best friends!"
I would almost be willing to accept the notion that Batman was just shocked out of his insanity by the sudden realization that hey, Superman has a mom too! Except just a few minutes earlier Batman was berating Superman, saying something about "Did your parents tell you you were special and had to save the world?" (Horribly paraphrased and possibly way off, but definitely involving his parents.)
So Lois Lane shows up and helps negotiate the truce. Batman runs off to save Martha while Superman runs off to confront Lex. Meanwhile Lois Lane takes the spear, the one weapon on the entire planet that we know can hurt Superman, and finds a deep watery hole to drop it in.
WHY WOULD YOU DO THAT?
If you have a single weakness you don't just leave it lying around somewhere hoping that no one else will find it! You hold on to it until you can stick it someplace as safe and well guarded as you can make it! Even if you're not aware of the impeding plot!
So Batman rescues Martha, murdering a lot more people in the process. Superman shows up at Lex's place just as Doomsday is hatching.
So did Lex expect Batman to kill Superman? If so, what was he planning to do about Doomsday? Did he think because it had some of his blood in it that it wouldn't hurt him? Given how Doomsday immediately went after the only other Kryptonian on the planet it throws some doubt on that "blood is thicker than water" notion. And if Lex didn't expect Batman to kill Superman why did he even bother setting up the fight? I understand the notion of arranging things so that "all paths lead to victory", but not so much so that "all paths lead to getting smooshed by one super-powered Kryptonian being or another."
Anyways, one way or another Superman ends up temporarily incapacitated while Doomsday is blasted out of the city limits. Then Batman realizes that they need the kryptonite spear to kill it, and instead of fetching the spear himself or sending someone else to do it, he decides to lead Doomsday back into the city. There's some kind of comment made about "the port is abandoned at night", but that seems like a very vague and handwavey justification.
So at this point Wonder Woman shows up. Prior to this she'd been wandering in and out of the film in her mortal disguise. Oh yes, but just before this she stopped to take a minute or two to watch the trailer for the next Justice League movie. The trailer itself was kind of dumb and poorly timed, and also the point at which they decided to show that trailer in the movie seemed rather dumb and poorly timed.
But ANYWAYS, Wonder Woman is here now! And she kicks ass! Then Superman shows up! Then Superman and Batman have an aside a brief about which of them is responsible for the presence of Wonder Woman (insert side-eyed smiley here, because LJ doesn't like the angle brackets)
So then they get into classic trailer formation and the movie goes into classic 300 slowmo so the audience can go "HEY LOOK IT'S THAT POSE FROM THE TRAILER!" Then the fight happens.
They aren't making much headway until Lois Lane makes a poor attempt to retrieve the spear and gets trapped, and Superman has to go rescue her, and in the process realizes "Hey! We could probably use this spear to kill Doomsday!"
So he gives the spear to Wonder Woman and she kills Dooomsday. The end!
...no, wait. He decides to use the spear himself, even though he realizes that just being near it significantly weakens him and will probably get him killed. Lois Lane also realizes this, so they have a tearful goodbye. Then Superman stabs Doomsday with the spear and gets stabbed himself, and they mutually die. (Strangely, Doomsday doesn't actually die until the spear goes all the way through him and the kryptonite is removed form his body. You'd think having the kryptonite still impaling his heart would be more damaging, but whatever.)
So now Superman is dead. But it was so dumb that i don't really case. Also we know that Superman has died and come back to life before (in the comics, after he was killed by... Doomsday.) Then even though we've seen sunlight provide miraculous healing power to Superman before, instead of sticking him under a sun lamp they decide to bury him in a grave.
We then get to sit through a couple long slow funeral scenes. (For both Clark Kent and Superman of course.)
And then just before the credits, we see the dirt on the coffin start to levitate, just like when Superman is about to fly... cut to black.
And there was no post-credits scene. You're going to give away that Superman isn't really dead (shock! surprise!) and you're not even going to save it for the post-credits scene? WTH?
Edit: Oh yes, one last thing. Why is Gotham right across the river from Metropolis? Putting two such large and distinct, er, metropolises right next to each other seems weird. And how does the canonically massive amount of crime in Gotham not spill over into Metropolis? And why was there a giant Wanye Tower in Metropolis? Do corporations headquartered in Kansas City, MO also have large buildings in Kansas City, KA and vice versa?
Also, you know that scene in the trailer where Batman is holding a gun and lots of people freaked out about the fact that Batman was holding a gun and Batman doesn't use guns?
You can relax, that wasn't a real gun. It was just a launcher for the kryptonite gas grenades. Batman is only murdering people with guns in all the _other_ scenes.
Also Edit: And at the end, Luthor knows about someone who those in the know say is almost certainly Darkseid, another major Superman villain. How does he know this? When did he know this? Is knowing about Darkseid what was causing him to go gradually insane over the length of the movie? Or did he only learn about it when he accessed the kryptonian computer? Is he intentionally serving Darkseid or did he think what he was doing would somehow help? It seems like it was really just a clumsy plothook thrown in for the sequel(s) without any real attempt to tie it in with the rest of the movie.
But seriously, i am nowhere near as good at snarking as Rob Bricken, you should go read his (also spoilery) version instead: