(Although it is messy and you have to let it dry overnight)
Thick, hardcover book in relatively good shape that you don't mind destroying and won't look too out of place on a bookshelf (check resale shops. Also, if you find one with pictures in the right places, even better!)
Exacto knife/utility knife
First, while the book is closed, use the sponge brush to spread mod podge along the three outside edges of the pages. To make the paste more secure, fan the pages a bit to make sure the mod podge gets between the pages (but just on the edges). Once you have a descent layer of adhesive on the pages, set something heavy on the top of the book and leave it overnight to let the adhesive dry and paste the pages together.
Once it's dry, lift the front cover (and a couple pages, if you want) and decide how big of a space you want to cut out. I generally cut out the whole page, leaving approximately a 1/2 inch on all sides. I do not recommend cutting within a half inch of the edges of the pages! Cuts don't always stay straight, and you may accidentally cut through to the outside of the pages.
Using your knife, cut the shape you want into the first few pages (the knife will only go through a few pages at a time, easily). These pages can be peeled up and removed (see pictures). Once they are removed, you continue cutting down, removing a few pages at a time until you reach the bottom (or however deep you want to go).
After you're done cutting, you may want to add another layer of mod podge to reinforce it, both inside and out. I added another layer on the outside, but not the inside, since I liked the feel of the paper.
Once it's dry, you have your very own, innocuous hide-away book compartment!