You can go through and complete a pre-approval application through your local public housing section. You may also want to document family size and income so when you reach the top of the waiting list you are prepared.
Not just anyone can get income-based apartments, since it is geared toward low-income people and families. You would be required to provide your income information to prove that you qualify to live...
Yes, they do have low income housing in every state. It is based off your income, and your bills are also calculated based on this number. You would have to show your tax info.