Katy is my..

Second cousin, if your father and her parent are first cousins; third cousin if your father and her parent are second cousins, and so on.

If you are in the same generation, you just add 1 to the degree.
Children of 1st cousins are 2nd cousins.
Children of 2nd cousins are 3rd cousins.
Children of 3rd cousins are 4th cousins.
and so on.

Removed is when you are not in the same generation. You keep the degree and add one "removed" for every generation.

Your dad or mom's 1st cousin is your 1st cousin once removed.
Your grandparents' 1st cousins are your 1st cousins twice removed.
Your great grandparents' 1st cousin is your 1st cousin three times removed.

And so on - if the cousin is a 2nd, 3rd, 4th - or a 12th, for that matter - again, you keep the degree and add removeds.

Removeds go "down" family trees too. If your 1st cousin has a child (grandchild), those children will be your 1st cousins once and twice removed.