The first part I made was the mouth. The way I build a mouth is to cut out the palate of the mouth from 1/2 foam. I then reinforce what becomes the top and the bottom of the mouth by gluing on 6mm craft foam. To this I add tubes made of 1/2 foam. Usually these are finger tubes but in this case they will recieve the top and bottom mouth bars on the rod mechanism. These tubes are then reinforce with fabric. The last thing you want is the tubes coming unglued in the middle of a performance.
Once the mouth was made I was then able to trim and shape the top and bottom bars on the rod mechanism.
Next came the construction of the head. I used 1/2 foam and a pattern of my own design. I've made a few puppets with other people's patterns before so I had a fairly good idea how to get the shape I wanted. I just had to do a bit of fussing to achieve a product I was happy with. If you're just starting out building puppets I recommend using someone else's pattern as a starting point. I've put a list of some links to free patterns which are currently available on the web. These are great for getting you started. Once you feel like you understand how foam works you can get creative and make your own.
As you can see with this head I made the top and bottom separate. I did this to make it easier to insert the rod. It turns out that this was unnecessary as the rod comes in and out with the head completely assembled.
Below are pictures of the head with the rod inserted. The first is with the mouth fully open and the second is with the mouth closed.