Core of giant star during hydrogen shell burning After the Sun runs out of hydrogen fuel in its very center, it will have a core of helium. The hydrogen around the core will be compressed, heat up, and star to fuse in a shell around the helium core.
Evolution of a star This shows a summary of the evolution of a star similar to the Sun. (1) The star spends most of its life fusing H to He in its center (core). This is called the main sequence phase of the stars life. (2) After its core H is used up, the core contracts, heats up, and H ignites in a shell around the non-fusing He core. The core and the rest of the star kinda go their own ways. The core continues to heat up and shrink while the remainder of the star expands and cools off, becoming a giant star. (3) after more contraction and heating, the core helium starts to fuse into carbon and oxygen (4) for a while, the star is burning He in its core and hydrogen in a shell (5) after the core helium in used up, the star has a non-fusing carbon+oxygen core and shells of helium and of hydrogen that are fusing.
In a star of mass below about 8 solar masses, the core never gets hot enough to fuse C and O into heavier elements. The two-shell fusion is unstable and the energy rate goes up and down widly, leading to a expulsion of the outer parts of the star into a gently expanding gas cloud called a planetary nebula. The central C+O core becomes a white dwarf stellar remnant. The white dwarf is sometimes called a star, but it has no fusion, so strictly speaking it is not a star. It does glow from the leftover heat it has. A white dwarf will slowly cool over billions of years.
Sun as a red giant star At its maxiumum extent as a red giant star, the Sun may be as large as 2 AU in diameter. The Earth would be about at the surface of the Sun. Of course, long before this, the Earth's surface would have been heated to the point where all the oceans were boiled away and all the atmosphere stripped away.
The exact details of how large the Sun will become are not known. This all won't play out for another 4 or 5 billion years, so no need to lose sleep over it!
Long range planning for you business majors
These are two examples of planetary nebula, clouds of gas gently blown off a star like the Sun in its last stage of evolution. In the middle of the nebula is a white dwarf, an object about the size of the Earth, but with the mass of several hundred thousand Earths.
White dwarf density A cubic foot of white dwarf stuff would weigh 1500 tons on the Earth- about the mass of all the cars in a Walmart parking lot on the 23rd of December. Here I am picking up a cubic foot of the stuff on a white dwarf (yea, right, DrBill)
Relative size of some objects These are sizes, to approximate scale, for the Sun (just the edge is shown - the entire Sun would of course extend far beyond the image), the Earth, a white dwarf , and a neutron "star". The neutron "star" should be smaller to be at true scale with Earth, but then it would be hard to see on this image.