Once you have a house, you will have to be given permission to place the house within the city. Once you have permission, you will have to perform a few extra steps.

Double click the house deed to see if you may place the house. If the house appears "green" you may click once to place it.

If you cannot place the house, move to an area in which it appears to have few or no building around it.

Once you place your house, you must declare residency. Go inside your home and find the terminal. It will be placed next to your doorway. Hold the mouse cursor over the terminal to get a radial menu.

You will have 3 options to choose from. Examine, Management, and Permissions. Move your cursor over Management and declare residency. This means you are now a member of the city.

You must go under Management again to pay maintence. Your house requires some money to keep it running. I recommend paying 1000 credits.

Once these two things are done, you have your first home.