Here's what I do:
Draw shapes on dull side of freezer paper. Stack 5 additional sheets of freezer paper underneath, all with dull side up. Iron around the outer edges of the freezer paper to glue all the stacks together. Cut out the drawn shapes with scissors. This means I get 6 shapes for every one I draw and cut.
If I were to use a printer for the shapes, I think this is what I would do. Print shapes on lightweight typing paper. Use a glue stick to affix to the dull side of a sheet of freezer paper. Stack 5 additional sheets of freezer paper underneath, and proceed as above.
6 sheets of freezer paper is the max for me in order to keep the cutting accurate.