The passive solution
Put paper towels, tissue paper, toilet paper or anything that absorbs water well between every single page that got damp. Make sure that part of the paper towels stick out of the book to transport moisture from inside the book to outside.
Close the book and turn it so the damp side faces down.
If possible, but a sturdy board that is ...
Freeze your book.
I did kind of remembered it, a google search did confirm it, this is the first site I found. This PDF file from a university an other.
If the getting wet was from clean water you should put your book in the freezer as soon as you can, and leave it there for a while. No need to package it, if you leave it in the freezer till it is dry you do ...