Methods Suggestion
Hello there!
Good to hear that construction is still alive and kicking
In reference to your question, what has worked for me in the past was either a) a reeeeally sharp pair of scissors (the ones that seem outrageously priced - not all of them, but look into Fiskars stuff) or b) surprisingly, a bread knife or a dull bladed knife. Or alternatively you could just get one of those 'scissor-guides' like they use to cut various materials at fabric shops and attach that to a flat surface. I guess my next question should be "what type of foam are you using?"
Different products have differing shears (ranging from a nice, clean cut, to just plain raggedy). I just used standard polyfoam (about 3/4") for my first few tries, and that cut really well with scissors (BTW, if you can't find one in the size you want, get thicker than you need, and then just slice it in half with whatever method works for you. I hope I could help! Keep on chugging along - I'd love to see your finished product!
Oh, and also, about your 'saggy puppet' issue, for me personally, I don't necessarily build my puppet around the foam. I build what will work with my hand, and just use the foam as a basic structure supported by my hand-work and the batting that I put into it. When I (finally) post my puppet images (i posted that really long yarn about my attempt), that'll give you a bit of insight into my methodology, although a lot of it is interior work. Post your pics when you finish!
Waiting to see the result,
Adam