by hand with a knife... we just did a half dozen "dancing couples" on coroplast that I had to cut out by hand (what a pain!!!) but if you have knife skills then foamboard would be a lot easier.
Now if you are talking lettering... well good luck with that I don't know of any way to diecut it and it would be a nightmare to try to cut out exactly. Maybe someone else has a trick for it...
Alot depends on the cutter you have. Some machines will cut on rigid media, which can give you an outline to trace with your knife. This is how I die cut my magnetic signs (i.e ribbons, scrolls etc)
The cutter cuts about halfway through the medis and I finish it off with a good knife.
If your cutter does not cut rigid material, the it's the old fasioned way like the rest of us.