If Andy was married to your sister, he would be your brother-in-law. As it is, he is married to your cousin, so he is your cousin-in-law. That isn't a real relation, but it's awfully fun to say. My cousin-in-law Cindy and I say it all the time. ("Hi, Cousin-in-Law! What's new?") To be related you have to have a common blood ancestor.
A full cousin is the child of your full aunt or full uncle. A half-cousin is the child of your half aunt or half uncle. (Your half aunt/uncle would be the half sister or half brother of one of your parents.)
> And so I guess she is married to Andy Samberg!
Wikipedia says she is. If his Joanna Newsom is the same as yours, your are indeed Cousin-in-Law. The fact they didn't invite you to the wedding says that you are not that close, but you could still send them a silver pickle fork and your congratulations.
The same source says of Joanna, " Her mother, Christine (née Mueller), is an internist, and her father, William Newsom, is also a doctor". So, if she is your first cousin, they are your aunt and uncle. If not, you may be second cousins, first cousins once removed, or something else. We generally don't get specific with cousin-in-law; "Second cousin once removed in law" would not be fun to say.
Please don't forget to choose a best answer. It doesn't have to be mine. 10 points aren't much, but they tell us you read the answers and we didn't flush 8 minutes of research and/or typing down the toilet.