Two hints on working with foam core:
1) You need a VERY sharp knife to do proper cuts. X-acto blades are fine except they will only be good for a few cuts and they are very expensive. Instead, use single-edge razor blades. You can get a box of 100 for just a few dollars. Don't be a hoarder like me--use them once or twice and throw them away. This is the secret to good foam-core work.
2) Hot glue works extremely well with foam core. Running a bead along the inside of right-angle joints is quick, rigid, and permanent. Best to use low-temperature glue--it is possible to melt the foam. Use the glue gun like a caulk gun: PUSH the glue ahead of the nozzle to get a nice, smooth bead.