How does general relativity explain gravity?

[Ryan_J]

I understand that general relativity gives us a different picture of gravity than Newton did. Instead of a force, it's the curvature of spacetime. But how exactly does mass curve spacetime? And how does that curvature then affect the motion of objects? What's the difference between general relativity gravity and Newtonian gravity in practical terms? Also, how do gravitational waves fit into this picture?