How did they get off the moon during the lunar landing?

The Lunar Module (LM) was basically two spacecraft. The Descent Stage had a powerful engine and large fuel storage (as well storage of all the equipment the astronauts would need while on the surface), used only during the landing. The Ascent Stage, which had its own separate rocket engine, contained the cabin where the astronauts flew during take off and landing, and slept between EVA's. At the end of the ground mission, the Ascent stage separated from the Descent stage, leaving that stage behind, and returned to orbit.

See the link below, which shows a picture of the separate stages.