What makes a step in a reaction not reversible? I'm learning all these mechanisms and having to memorize which steps are reversible. Is there a way to figure out whether it's reversible or not?
There's no way of figuring that out "from scratch", it is a lot of experience and knowledge. There is no general answer to this but there are some steps which are basically always seen as reversible or irreversible*.
protonation/deprotonation: unless an extremly strong acid/base (like BuLi) is involved those are always in some kind of equilibrium and are reversible.
exchanging a good leaving group with a bad one: That can be seen as irreversible.
gas evolution: as @LinearChristmas pointed out: that can be seen as irreversible (if you are working in solution)
in general: producing a stable structure: for example aromatization, that's irreversible
*theoretically every reaction is reversible, but if the equilibrium is far on one side we call it irreversible.
For an explanation what makes a reaction reversible see: Is every chemical reaction in equilibrium?