Newton's laws of motion

The first law is inertia, the second says force equals mass times acceleration, and the third says forces come in equal and opposite pairs. They were published in Isaac Newton's Principia in 1687.

It means an object's acceleration depends on the net force applied and its mass. A 2 kilogram object pushed by a 10 newton net force accelerates at 5 meters per second squared.

Your foot pushes backward on the ground, and the ground pushes forward on your foot with an equal and opposite force. That forward friction force is what moves you ahead.

Yes, they work extremely well for everyday speeds and sizes. Einstein's relativity becomes necessary near light speed, in strong gravity, or for very precise measurements.