Common Ancestor	Child	Grandchild	Great Grandchild	Great Great Grandchild	Great Great Great Grandchild
Child	Sibling	Niece or Nephew	Grand Niece or Nephew	Great Grand Niece or Nephew	Great Great Grand Niece or Nephew
Grandchild	Niece or Nephew	First Cousin	First Cousin Once Removed	First Cousin Twice Removed	First Cousin Three Times Removed
Great Grandchild	Grand Niece or Nephew	First Cousin Once Removed	Second Cousin	Second Cousin Once Removed	Second Cousin Twice Removed
Great Great Grandchild	Great Grand Niece or Nephew	First Cousin Twice Removed	Second Cousin Once Removed	Third Cousin	Third Cousin Once Removed
Great Great Great Grandchild	Great Great Grand Niece or Nephew	First Cousin Three Times Removed	Second Cousin Twice Removed	Third Cousin Once Removed	Fourth Cousin
EXAMPLE: A "first cousin" is your relationship to your parent's niece or nephew, because you are both grandchildren of a common ancestor.
Your relationship to your cousin's child is "first cousin once removed", because you added one generation to the relationship.
However, the relationship between your child and your first-cousin-once-removed would be "second cousin", because they are both great-grandchildren of a common ancestor.
The chart can be expanded for as many generations as necessary.