Saitama initially lived by himself in the apartment building, before Genos moved in. The apartment resides in the middle of Z-City's ghost town, therefore Saitama is the only resident there. The apartment is small with a large living space, small kitchen and bathroom. Genos pays rent money to Saitama to live there.
The following section contains Webcomic spoilers. You have been warned, manga-only readers.
During the Monster Association battle between S-Class heroes, Tatsumaki used her powers and destroyed the whole area, including the apartment. Saitama later got promoted to A-Class hero and moved to A-City headquarters.