James, welcome to the wonderful world of marquetry!  I know some people have long arm scroll saws or a frame saw that has a large table that can get the job done. As I don't have either I cut the parts out and carefully tape them in place on the field and then use a scalpel to cut them out. When they're taped down all you need is a light score around the piece and then you can remove them and finish the cut.  I used an Exacto knife for a long time but after using a scalpel I found there is a big difference in sharpness. Also, when you're cutting really small pieces it is a good practice to have veneer tape of some sort as a backer because those little pieces can get really fragile. I was looking for pics to show how little tape I used to hold them down, but I guess I don't have any. Here are a few pics that I took of the process and in one you can see I actually assembled the flowers on green tape so they would have a backer but then I had to cut around that tape with scissors, there has got to be a better way!  I hope that helps and if anyone else has a better or different method I would love to hear it. 

-- Paul--- Creativity is allowing yourself to make mistakes. Art is knowing which ones to keep. — Scott Adams