Richard,
If 23AndMe is predicting a 1st cousin, it means that the amount of DNA you share with that person is equivalent to what you would expect to see if you shared a full set of grand-parents (i.e. 2 grandparents) in common with your match. If you only shared one grandparent, then you would only share about half as much DNA with this person, and would not be predicted to be a full first cousin match. The best way to verify whether this 1st cousin is connected to you through your mom's side or your dad's side would be to also have your mom tested on 23AndMe. If the match is through your mom's side of the family, then she will share about twice as much DNA with the match as you do.
Claudia Bullock
