While just about everyone has heard mention of cousins once or twice removed, the majority of people are not quite sure what that means. Although it sounds complicated, it's really only a matter of simple generational differences. Calculating the cousin relationship between two individuals, even when levels of removal are involved, takes only elementary math and is not difficult once you understand how it works.
Determine the nearest ancestors that you have in common with the other person. This can be done by tracing both your ancestry and the other person's until you find the point where your family trees overlap. You may be descended from the same set of great-great grandparents, for example.
Count the number of generations between yourself and the common ancestors, then do the same for the other person. If these numbers are the same, the two of you are from the same generation, which means that your cousin relationship will have no removes.
Add one to the number of "greats" in your common ancestor's title to figure out your cousinship with the other person. For example, if you share the same great-great grandparents, by adding one to the number of "greats" you can determine that you are third cousins.
Calculate the degree of removal if you and the other person are from different generations. This can be done with simple subtraction. If there are three generations between you and the common ancestors and five generations between the other person and the common ancestors, subtract the smaller number from the larger number, which in this case will give you two. Then add one to the number of "greats" in the closer relationship, which is yours in this example, the ancestors being your great-grandparents while they are third-great grandparents to the other person. By doing this, you can determine that the other person is your second cousin twice removed.