I understand that Gravity will effect on space-time and create a curvature, which tells the mass how to move, therefore, the SUN can rotate smaller objects because it has stronger gravitational pull. I also understand that the sideways velocity keeps the Earth in its rotation circularly.
What I can't understand is: How curvature of Space-time moves the Object? How for example Curvature of space-time for Sun and Earth Looks like?