It will come naturally the more you do them. There are really only a dozen or so basic mechanics in dungeon fights and they just get recycled/slightly tweaked throughout the game. There are some dungeons that have somewhat unique mechanics, but often time their uniqueness makes them easy to remember. Overall, just use good judgment and you'll usually be fine.

And don't feel bad if you don't remember. I don't think I've run Sohm Al once without at least one person who can't remember which jellies do what on the Dinosaur boss. It's perfectly fine to say "I don't remember this very well, anything to look out for?"

edit: Also, if a boss has a really annoying mechanic, a lot of times a party member will say "oh, this asshole" or something to that effect, which is your cue to ask about the annoying mechanic...