How do I figure out if someone is a first cousin, second cousin, cousin once-removed, etc?
Count up the generations from the first person to the first common ancestor, and from the second person to that common ancestor. Subtract one from the lower of the two values to get the degree, and the difference between the two values is the number of times removed.
So if person A has a great-grandfather who is person B's grandfather then they would be first cousins, once removed. Likewise if A had a great-great-grandfather who was B's great grandfather then they would be second cousins, once removed.
More, much more, can be found in the wikipedia article on cousins.
Cousin (a.k.a "first cousin")
Your first cousins are the people in your family who have two of the same grandparents as you. In other words, they are the children of your aunts and uncles.
Your second cousins are the people in your family who have the same great-grandparents as you., but not the same grandparents.
Third, Fourth, and Fifth Cousins
Your third cousins have the same great-great-grandparents, fourth cousins have the same great-great-great-grandparents, and so on.
When the word "removed" is used to describe a relationship, it indicates that the two people are from different generations. You and your first cousins are in the same generation (two generations younger than your grandparents), so the word "removed" is not used to describe your relationship.
The words "once removed" mean that there is a difference of one generation. For example, your mother's first cousin is your first cousin, once removed. This is because your mother's first cousin is one generation younger than your grandparents and you are two generations younger than your grandparents. This one-generation difference equals "once removed."
Twice removed means that there is a two-generation difference. You are two generations younger than a first cousin of your grandmother, so you and your grandmother's first cousin are first cousins, twice removed.
I've found this chart to be the most helpful for me and I keep a copy in my research notebook.
If looking at charts makes you dizzy, try the Relationship Calculator on Stephen P. Morse's One-Step Web Pages.
FULL, STEP, AND HALF RELATIONSHIPS
Full Siblings: Two people having both biological parents in common Half Siblings: Two people having only one biological parent in common Step Siblings: Two people having no biological parents in common but one of each of their biological parents marry each other.
If you have half- or step-relationships, see the notes below the input boxes:
There is no way to enter a half relationship on this calculator, so it will never report a half result. To enter step relationships on the calculator, type parent's-spouse's child instead of parent's-child. It will report a non-blood result, which implies the step relationship.