Well, at least you tried. Here comes the mighty anon, on a mission to correct!

The suns fuel is the hydrogen that it mostly consists of. There's also quite a lot of helium, but that's the product of the fusion that makes the sun, well, burn. In several million years, there will come a time when there's no hydrogen left in the star to fuse. It will then start fusing helium and other, heavier elements like oxygen and coal. When this happens, the outward forces inside the sun will force the outer layers to expand and turn the sun into a red giant. While in this state the star will be pumping out obscene amounts of gas into the universe (oh, by the way, it has already swallowed earth) which will in time become a nebula and give birth to new stars. When all the gas from the outer layers has been expelled, only the core will remain. The core, the only remains of our sun, is now what is commonly known as a white dwarf, about the same size as earth was, glowing due to the extremely high surface temperature (about 100 times the current surface temperature of the sun) and will continue to glow for billions of years. When it has cooled down, it'll become a black dwarf. A black dwarf has never been observed and is only theoretical, since the estimated cooldown-time for a white dwarf is about 20 billion years - more than six billion years more than the time the universe has existed.

Questions?

It is not so much the Sun running out of fuel so much as what are the ratios of Hydrogen to Helium within the Sun's core. Helium is a byproduct of the initial primary fusion cycle used to produce energy within a star the size of the Sun. As this Helium accumulates, it forms an inner core.

This inner Helium core becomes dense enough as the Sun ages that it's gravity acts on the Hydrogen layer above it, increasing the rate at which the Hydrogen fuses. This increased fusion rate/ energy output in turn causes the convection layer above the Hydrogen layer to expand, occupying a much larger volume. Thus all the layers above that one must expand also.. This massive increase in volume in turn drops the effective temperature of the outer most visible layer of the Sun (photosphere) down to where the peak output of light is in the red range of the visual spectrum.
The Sun will continue to evolve as it enters the Red Giant phase. The Hydrogen layer will be depleted at a faster rate until the degenerate Helium core reaches temperatures/pressures sufficient to commence the Helium fusion cycle.