Methods of implanting a prosthesis to repair a joint include displacing a first bone from the joint formed by an intersection between the first bone and a second bone. An end portion of the first bone is resected to define a resected end. A concavity is formed into the resected end using a shaping tool. The bone is compacted to form a support layer lining the concavity. The prosthesis is implanted in the concavity against the support layer without attaching the prosthesis to the support layer. The joint is reformed with the prosthesis such that the prosthesis remains unattached to the support layer and the first and second bones articulate about the prosthesis.