Question

What causes objects to move or stay still?

Answer 1

Force or forces (in physics: net force)

Answer 2

If it is still, it will tend to remain still, due to inertia. But a net force would start it moving. 
If it is moving, it will tend to continue moving, due to inertia. But a net force, in the right direction, could cause it to stop. But if that force continues, it will start moving in the opposite direction.

Hope this helps  :)