I have a friend who is a single mother working a low paying job. Her income is a barely enough to feed her and her child let alone pay for the rent. She has told me that she wanted to move to a better place with better schools but usually the rent in those area are too high. I told her that it would be possible to rent in better areas if she chose to live in low income apartments for rent. These types of apartments are subsidized by the government so that the renter would only have to pay part of the rent while the government covers the rest. The money is given directly to the apartment owners and the owners agree to lower the rent.
I suggested that she visit a HUD housing office to get more information on this. In order to qualify for HUD apartments, your income must be at or below a certain limit. Every state has a different limit so you would have to get the information from the housing agency. For example states might impost that income should not exceed 30% of the median income of the city that you living in. Once you have figured out whether or not you would qualify for low income apartments, you can then begin your search.
On the HUD website you will find an apartment search tool that allows you to find the exact apartment that you want. First you will be asked which state you are looking for. Then you can select a city, county, or zip code. You can also look for apartments with specific number of bedrooms. Once you get the information about the apartments you should contact them and find out if they have availabilities. Many times the apartments will not have vacancies which mean you could be put on a waiting list. You could be put on the waiting list for several months before there is an opening. It would be a good idea to get on several waiting lists for different apartments.
My friend put her name on the waiting list for a couple of subsidized apartments. In the meantime, she is sharing an apartment with another friend.