You can start by going on line and check for HUD in your area. As r010159 said there are often waiting list, it depends on where you live and the need in your area. You can also call 411 and tell them you are looking for safe affordable housing they might be able to help with some ideas. Also if you have a way to see a SW, you can ask if there are any programs in your area to help those with MI, find safe affordable . There usually is a priority list for need. Most of these programs have a % of your income that you pay, it's something like 1/3 of your income or less. Most apts are more than 50% of disability checks.

So the one thing you will need a lot of is patience, and a lot of it, for this is bureaucracy at its best.