Hi Rachel
If you go out and look a the stars from a dark location you can see with your eyes that the stars are different colors. In the past before there were artificial lights at night most people could do this, so I think people have known for a long time that stars are different colors.

The colors do not directly tell us about the age of stars. That was only possible after people had studied the stars and their spectra. Spectra spread out the light into different colors, so you can see in detail how the colors vary. There are features in the color of stars that help scientists figure out the temperatures and other aspects of the stars. These combined with other observations of the stars allowed researchers to come up with an over all theory of the life cycle of stars and allowed them the figure out where they thought different stars are in that life cycle.

One of the important early researchers into star spectra was Annie Jump Cannon. You might like to read about her:

http://www.sdsc.edu/ScienceWomen/cannon.html
cheers,
Terry