Hi Spencer,
It turns out nuclear fusion is a _very_ efficient source of energy and the Sun is very big. As a result it can go on a long time. Not eternal, though. Billions of years seems like a long time to us, but it is not forever. The hydrogen in the Sun's core is very slowly converted into helium. Eventually there is not enough hydrogen to burn and we expect it to start burning the helium to form carbon and oxygen.
Whenever a star uses up a particular kind of element in its core it starts to contract - with that fuel used up the core cools and there is less outward pressure to keep the outer layers of the star from falling in. Then, pressure at the center increases because of all the material falling inwards. Eventually there is enough pressure to start fusing the heavier elements in the Sun's core, which heats up, and the outer layers of the atmosphere expand again so that the star is large than before, but with a cooler, redder surface. This is called a red giant star.
Observing this from the Earth would take a long time, and it would also be pretty unpleasant. If Earth is still around at all its atmosphere would probably boil off. Eventually for a mid sized star like the Sun the outer atmosphere of the star will fluff outwards leaving a small, white-hot core called a white dwarf. A white dwarf is about the size of Earth.
Stars larger than the Sun can eventually turn into even stranger things like neutron stars and black holes, but I won't go into that here.
You can find out more about all this here:
http://www.windows2univer...uff/tourstars_1.html
cheers,
Terry