An addendum to the first couple of replies: Developing exposed film into negatives at home is fairly straightforward and doesn't require a full darkroom (just a dark place -- even a closet or changing bag -- in which to load the film into a tank). Creating prints from negatives, though, does require a full darkroom, although it can be as simple as an enlarger and developing trays in a bathroom. (Scanning and creating prints digitally is another option, but one that's off-topic for this forum.) If you want to just "get you feet wet" with film processing, buying a tank, some chemicals, and a few odds and ends and doing the film developing part at home is an option. If space is very tight or if you're not sure you want to invest the time and money into setting up a complete darkroom, though, locating a rental darkroom in your area may be a better option.
Unfortunately, I can't point you to any NYC-area rental darkrooms, although I'm sure some exist. Perhaps you could try your Yellow Pages under "darkrooms" or "photography."