The first thing you may notice when looking at a many 'Pop-Up-Book' is the very thick pages composed of double sheets of thin board or paper.  Obviously the pop-up part has to come from somewhere and if a single sheet were used there would be holes on the previous and following pages !

With some simple shapes a very attractive pop-up creation can be achieved and as with

any project in Design & Technology, it makes great sense to check out existing designs and analayse how any particular effect has been created.
These images here have been taken from "Beware of the POG!" by Kees Moerbeek and published by Intervisual books (ISBN 0-85953-239-9

STEP 2 -   A small extra fold in the main  fold will allow a reverse fold to be added. 
The bottom jaw of this picture shows this feature.

STEP 4 -   Following steps 1-3 and completing the construction with an additional small piece of card adds to an even  more impressive image.  The flat pig nose on this photograph is a good example.