So I just finished writing one of my best pieces: a jazzy space ballad. Now I am looking for vocalists to sing lead and backing parts. Where / how would I go about getting singers on an indie dev's budget (exactly $0.00)? Also, what would I need to provide singers? I have sheets for all vocal parts (separated in PDFs) and midi tracks of all parts as well as a recorded instrumental backing track. Anything else they would need? Thanks!

For $5 you might be able to get some on fiverr.com

You need to work on your contacts and networking.
Try looking for student or professional singers in your local conservatories and music colleges. Try talking to the teachers\instructors as well, as they may forward some people to you.

It's not impossible to find someone that would perform for free; some artists have that much passion for their field.
This depends, of course, on how fun you are to work with and if you can arrange a comfortable recording session (schedule, location etc.).

I myself don't know for sure what material a singer would need. I suspect the vocal sheet, the vocal melody track and an accompaniment track.
To get that information I would certainly ask the artist himself.