By reading historical accounts of what colors different things were.

If you give people black-and-white film to watch, people are guess the colors that are there based on what they are familiar with anyway, so this has a chance to be more historically accurate than that.

Consider the film "They Shall Not Grow Old" in which WW1 footage was painstakingly restored and colorized. They went and found old uniforms and weapons to check the colors. They went to the present-day locations to check the colors of the grass and trees. Etc.