I am trying to find out how to make a popsicle stick puppet like the ones in this Jib Jab Video:

http://sendables.jibjab.com/originals/2011_buh_bye

Specifically how to make a movable mouth mechanism....

Any thoughts wonderful puppet people?

Off the top of my head, an idea would be:

Cut out the image you want to use. Cut away the bottom jaw (use a scalpel) area and put it aside for the moment. Attach the rest of the image to the stick.

The mouth mechanism could be done with a string and elastic method. Attach the back of the head image to a short piece of elastic (ie. the elastic hangs down at the back where the jaw will go). The other end of the elastic gets attached to the back and top of the jaw piece. Attach another stick or a piece of string to the back/bottom of the jaw. Pull the string to make the jaw move; the elastic means the jaw will return to a default position after each pull.

(In thinking this through it would probably work best if not only the elastic is short but the two images overlap, so you're not seeing elastic when the jaw is pulled downwards)

This is entirely untested and off the top of my head, however a basic elastic/string mechanism would work so maybe modifications to my suggestion could be made. I sort of did something similar here:
http://www.puppetsinmelbourne.com.au/faq.php/2008/10/30/how-to-make-a-blacklight-puppet

Although it's not the same style of puppet, you can get a better idea of the elastic/string mech.

PS. Welcome to P&S! Nice to see another Aussie join the ranks.

Here is a pretty good how to on makeing a puppet like this. Has a video so you can see how it is done. http://www.helpimachildrenspastor.com/2010/10/make-a-working-rod-puppet-from-office-supplies/

That's a great link Shawn! And pretty much what I had meant to describe

Brilliant help team, thanks for your time and input!