When someone asks a "How?" question they are normally looking for a desdcription and when they as "Why?" they are looking for a mechanism. As graham.d explained above, nobody knows the mechanism. The desccription is given by Einstein's field equations.

The source of gravity is mass, which, as Einstein described it in his 1016 GR paper, is fullly described by the stress-energy-momentum tensor. Think of the EM analogy where charge is the source of the EM field. What is charge in one frame is current in another. Charge and current form a 4-vector and that 4-vector appears in the tensor form of Maxwell's equations. A similar thing happens in GR. What is mass in one frame is momentum and stress in another. The mass, momentum and current form a second rank 4-tensor which appears in Eisntein's field equations.