There is no one perfect way to build a puppet- I believe most builders experiment and find their particular favorite ways of doing things. It's part of the process- I find it fun to be able to figure out something or discover a new way of doing a step.
I have included a picture here of how I glue foam parts together. Lightly applying to both sides with a scrap piece of foam, then allowing only about 15-20 minutes to dry for the contact cement seems to work well for me. I apply the glue to all the different pieces in one setting- because usually by the time I am done putting the glue on the last piece, the first piece has had enough time to dry to stick together.