How does a star become a red giant?
Once a protostar forms, its life cycle is fixed.
For the first few billion years, the new star continues to shine as its hydrogen is changed into helium by nuclear fusion in the star's core.
But eventually most of the star's original supply of hydrogen is used up. By this time, most of the star's core has been changed to helium.
Then the helium core begins to shrink. As it shrinks, the core heats up. The outer shell of star is still composed mainly of hydrogen. The energy released by the heating of the helium core causes the hydrogen shell to expand.
As the outer shell expands, it cools and its color reddens. At this point the star is a red giant. It is red because cooler star shines red. And it is a giant because the star's outer shell has expanded from its original size.