BigBadWolf's method of using a chinstrap and mesh - http://fursuits.wereanimal.net/v2mask.htm

When you attach the elastic to the chinstrap, be aware that just about nothing will stick to it. Use a pin about the size of the sewing needle you're using to poke maybe 10 holes 1/4“ apart. That way, when you need to replace the elastic, just reuse the holes you made.

From: Rowan
Large clothing snaps make great hinges. The spidery ones will give either 4 or 6 points on each half of the snap to sew to the mesh of the head and the jaw. They give a very smooth and easy movement.

An added bonus is that you can unsnap the jaw during head construction while you are fine tuning the connection between it and your chin to better be able to get into it and sew.

Probably want to use stainless steel so they don't sweat rust and they might want a small drop of oil occasionally.

- shaped mesh
- sculpted foam

Marcwolf has used a simple method of a chin strap and a bar that the wearer can hook their chin under. The effect is that any movements of the wearers jaw is translated in the characters jaw moving. Due to the lever effect the jaw generally moves more than the wearer's. I used galvanised bolts and a spring for the hinger and tokeep the jaw under tension. The bolts have rusted due to sweat so I'd recommend using Nylon bolts where possible.
You can see that jaw design here http://marcwolf.org/construct/mask_web/index.html and the finished look here http://marcwolf.org/construct/realism/index.html