A rocket works because of two of the laws:
(a) action and reaction are equal and opposite
(b) momentum is conserved in an interaction
The simplest way of seeing this is to blow up a balloon and then let it go.
The balloon rushes all over the place as the air shoots out of the open end. It is behaving like a rocket - the ACTION of pushing out the air produces a REACTION that pushes the balloon forwards.
The momentum of the air is equal and opposite to the momentum of the balloon.
In an actual rocket it is the exhaust gases that rush out of the back. The velocity of these exhaust gases depends on the fuel used.
The rocket does not have to push against the launching pad, the reaction on the combustion chamber pushes it forwards. It is partly for this reason that rockets are able to operate in space.