Turns out DC has a chronology just like Marvel, and you really should watch "Man of Steel" (2013) before watching "Batman v Superman: Dawn of Justice." Actually, my suspicion is that you should NOT watch them: you can do that in either order, and you won't have lost five hours of your life.
In "Man of Steel," Superman's battle with General Zod badly trashed Gotham City. Now Batman (Ben Affleck) is all upset with Superman (Henry Cavill) and determined to take him down to end the threat of the untrustable alien. To which end he constructs a battle suit and makes some nasty Kryptonite weapons. Into this mix we throw Diana Prince (Gal Gadot) aka Wonder Woman, and Lex Luthor (Jesse Eisenberg). And here we hit upon the biggest of many problems with the movie: Eisenberg and director Zack Snyder have apparently concluded that "massively annoying" is the same thing as "massively evil" and substituted the former for the latter in Eisenberg's performance. I wanted to punch him every time he was on screen because he was so irritating. Let's compare this to Heath Ledger's performance as The Joker. Ledger was unsettling the second you saw him, and the air of menace about him was palpable. Punching him wasn't something you thought about: "getting the hell out" was more likely the plan. Eisenberg is a capable actor, but when he does evil things as Lex Luthor it seems more like a mistake than a plan: he's a very poor villain.
This is DC's equivalent to Marvel's "Captain America: The Winter Soldier" - they're starting to get a smaller group of superheroes into the same movie. There are several strategies at work here: 1) roll several superheroes together, see if it sells, 2) question the morality of one or several of the superheroes, 3) which allows superheroes to fight each other because everybody loves that, 4) save the world, 5) hint at a bigger group movie to come (the upcoming "Justice League" movie with Batman, Wonder Woman and more). ("Winter Soldier" was actually post-Avengers so the latter point doesn't apply, but the rest of the points apply to both movies.) I'm sick to death of the comic book penchant for changes of opinion exclusively so we can see a fight between this hero and that ("Captain America: Civil War" is the worst for this) and the team-up-and-save-the-world trope at the end has also been done to death. Superhero movies need to bring something new to the table to be interesting, and this one doesn't.