How do people figure out that they're color blind?

Comparison with peer. They usually discover this when they are in a situation in which color choice is necessary and they notice their peers making choices difficult or impossible for them. This usually occurs in school such as when picking crayons to color a picture or using colored papers and picking the wrong color for a certain task. Then they can be formally tested to determine the actual type.
Ichehara test. There is a set of color images that help determine that.