Well, rockets have multiple components that are necessary to get off the ground.
The basic model rocket uses these components to lift off of the ground:
1. A Bodytube
2. A Nose cone
3. Fins
4. A motor or engine

All of these components propell the rocket into the air. Thanks to Sir Isaac Newton, The third Law of Force and Motion helps determine how a rocket works. In his law, Newton states that every action has an equal and opposite reaction. What does this mean? Take a look at a balloon. The balloon is just filled with air, assuming you did so. Now you let go of the ballon and watch it fly all over the place. The air escaping from the ballon is moving backwards while the balloon itself is moving forward, thus giving you your equal  and opposite reaction. The air is "propelling the rocket into the air, as does a rocket's motor.

Now you must be wondering how the rocket returns safely to earth. Well inside the rocket, assuming you are using an Estes brand engine, the motor has a final release charge that, again going back to Newton's law, forces the parachute to push the nose cone out of the tube where the parachute is then released and deployed.