Specifically, how do Butler and Artemis find Holly?

After translating the Book, Artemis reads a passage that mentions a magic ritual which takes place under an ancient oak during a full moon at a twisted river. Artemis finds the ancient oaks that meet at a river bend in Ireland. There are 129 sights, so he and Butler begin to watch them. They have been doing so for four months when Holly shows up. Holly is there because she has no power left because she has not performed the Ritual.