What determines whether a step in a reaction is reversible?
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?