As our star burns fuel, its mass lowers, which lowers its gravitational strength. It's a little counter intuitive to think of the star actually getting larger as it loses mass, but the reason is because the lower gravity strength can't hold the sphere as tight as before.
As the sphere gets larger, and the fuel is consumed, the fire gets cooler. Cooler fire is more red than yellow.
The most famous Red Giant that I know of is called Betelgeuse (Beetle Juice), which is the top left shoulder of the constellation Orion. If you know somebody who can point out the constellation to you, you'll actually be able to tell with the naked eye that it is red.