Nutshell Rocket Theory:

Newton's third law: The law of reciprocal actions
Forces always occur in pairs. If object A exerts a force F on object B, then object B exerts an equal and opposite force -F on object A.

or

Whenever a body exerts a force on another body, the latter exerts a force of equal magnitude and opposite direction on the former.

A simple rocket consists of a combustion chamber and convergent divergent nozzle. The propellants in the combustion chamber are ignited, thus creating a high temperature high pressure environment. The gas rapidly expands and is accelerated through the convergent divergent nozzle. Thus, the product of the mass moving at some velocity is momentum, and whenever there is a variation in momentum a force will be generated. The high velocity exhaust gas will then impart momentum to the engine. This reaction is called thrust, the force that propels the rocket.

As long as the thrust to weight ratio is greater than 1.0, the force will be great enough to propel the engine. The thrust to weight ratio is directly proportional to the acceleration of the engine, so an efficient engine will have a high thrust to weight ratio. The engine will tend to accelerate until the engine velocity equals the gas exhaust velocity.

In a nutshell that is how a generic rocket works.