The visible part of the star swells up and cools down, forming a red giant. As the core goes through its fits and starts of fusion and burns its way toward the white dwarf stage, the outer part goes through a very unstable period, varying in size and brightness in ways which may be unpredictable. The planetary nebula slowly disperses into space, where the gas may eventually be recycled into another nebula to form another generation of stars. The white dwarf, very hot but very small, shines on for a while, radiating away all the heat it has stored up, and gradually fades away into a small chunk of extremely dense material called a black dwarf. This is the scenario for stars which start out being smaller than about 8 times the mass of our Sun.
Larger stars start their lives the same way, but end it much more spectacularly.
We'll talk more about that in the next unit. It turns out that mass is the most important factor in determining everything about a star.