Film curl is something I deal with in the projection room a lot.
Emulsion absorbs water at a different rate than the base. Depending on the humidity of the air and of the film/paper emulsion and base, it will exhibit "positive" or "negative" curl. If the emulsion is a bit drier than the base, it will contract slightly and cause a "positive curl" where the film curves toward the emulsion side. If the emulsion absorbs enough water (such as right after development and before it fully dries) it might have a "negative curl" where the film curls toward the base side.
Most films are designed to have a slight positive curl (toward the emulsion) when they are at 50% to 60% humidity. Most papers will have a slight positive curl as well. However, in my experience, you are less likely to see a negative curl in photographic paper because the base is more absorbent. Film base (acetate or polyester) doesn't absorb water. Resin coated papers also have a less absorbent base and, although will exhibit curl, it won't be as much as fiber based.
A lot of times, you can tell which side of the paper goes up by the feel. It's usually the glossier side. On matte finished papers, there is very little difference.
One trick the old timers in the projection room used to use is to slightly moisten your lips (or your finger tips) and pinch the film between them. The emulsion will stick to the moist surface more readily than the base will.
Take that advice with a grain of salt. Although the trick does work, ask yourself: "Do you really want to put film in your mouth?" It won't kill you but it's not exactly health food, either. Besides, who wants to get saliva splotches all over their film?
