The short answer is as long as possible, but rarely less than two weeks not including flights to and from Africa.

A well-rounded trip to Africa usually includes a safari lasting 3-4 days to see the big 5 (lions, leopards, rhino, elephant, buffalo), followed by a domestic flight to another part of the country where you can adventure to find lesser seen animals (for example: gorilla or chimp trek, or flamingos at Lake Turkana) finishing with a few days at the beach for some rest and relaxation. For those less interested in beaches, you can finish the trip with a rich cultural experience at one of the lodges or camps located on a conservancy focused on community and education.