I bought a sheel of foam core, but now I can't figure out how to cut it. Everything I try ends up damaging the foam and the cut ends up ragged and poor. Should I be using some sort of specialist tool for this?
I use a large hobby knife. Those little ones just don't cut it.
Also, you shouldn't expect to cut it on the first pass... or even the second or third pass either. First pass you might get through the paper, second pass, through the paper, and then after a few passes, maybe five, you are through or cutting the paper on the other side. As long as you cut slowly, you'll be fine even with a dull knife.
If you want to cut faster, with fewer passes, you need a very sharp knife. I find that after a few cuts, the knife gets too dull to cut quickly. But press lightly, and make a handfull of passes, and you'll be fine either way!

Thanks
n