Look for signs with a blue arrow on a white background that say Arrendador divisa. These indicate that the owners of the house host overnight guests. Professionalization is such that some welcomes can be a bit cold and remote, but sometimes you'll be received warmly, as if you were a long-lost cousin arriving for a family reunion.
Sites like www.casaparticular.com offer various places and other agencies are starting to make inroads on the island, but the Internet is still pretty shaky in Cuba. Local contacts are often the most effective: if an owner can't take you in, the chances are that he or she will know someone who can. You can also try to line up something before your arrival by contacting Fabio and Eugenio at Greenhouse or the Casa of Pepe y Rafaela but word of mouth is such that their rooms in Old Havana are usually fully booked.
Rooms: from 30 CUC