You track populations.

For example, if there is a gene variation that you see in African Americans, but not in people in Africa, and is more common in African Americans than in Americans not of African descent, then it probably originated in the American South; and depending on how distributed around the US is it and how many people have the gene variation, you might be able to guess how old it is.

A notable real-world case is a specific mutation in the Y-chromosome found in about 8% of Asia stretching from northern China to eastern Europe. Because it's on the Y chromosome, it's (almost) entirely male-linked; and the working hypothesis is that the gene originated in Mongolia (it's more common there), and spread with Genghis Khan's conquests. The fact that this gene shows up more or less the same amount over such a wide area suggests that it showed up about the same time in all those places - and Genghis Khan explains that nicely.