I'd like to replace the existing light in the stall shower. What do I need to know about the fixture? Where can I get such a light?

Both Lowe's and HomeDepot (and probably Sears hardware too) have lighting meant for wet locations:
http://www.lowes.com/lowes/lkn?action=productList&N=0&Ntk=i_products&Ntt=shower%20light

Look for the term "wet location approved" on the packaging.

All I have to add to rick's answer, is that a fixture rated for damp locations is acceptable for a shower, and any fixture installed in a shower needs to be GFI protected.

You will find both the housing and the trim must be rated for damp locations.