Does anyone know how subsidized housing works?

First of all i have to say, I do have a job. I just got over a break up and I am staying with my mom :--(. I was looking for some additional help to find me and my son a place. I am living off of only my income, my sons father is deceased and didn't work enough quarters for me to get social security for my son. I just needed to know how it works and the amount of rent I would have to pay. I make $2742.40 a month before taxes. If anyone has any information I'd really appreciate it.