How would one care for the skin that is in contact with the prosthesis?

Protect it. Cover it with a padding or protect it from the prosthesis. Otherwise, over time you will get a significant "scar" or callus of the area.
As usual. The skin that is inside a prosthetic socket needs to be cleaned as usual, with soap and water. Generally speaking this skin, especially in the leg, tends to get dry so a good lotion or cream used everyday is helpful. It is as important to clean prosthetic liners/socks sockets. Wash all areas/parts in contact with the skin everyday.