I've been trying to figure this out, but I must have missed some little key detail. Here's what I know for sure.
Quentin and Julia are traveling through Fillory, exploring the islands. By the power of the magic keys, they accidentally return to Earth. After 3 days of trying to get back, they finally end up at the place where people were first able to go to Fillory, and somehow after a whole day of searching end up back at Fillory, first trying each of the methods outlined in the books for entering the place.
Thanks for the help!