I started ironing the pieces of freezer paper to the fabric. I cut them out and fit them together as I go so I don't forget which piece goes where -- they look a lot alike when they're cut apart. I guess I could have numbered them to make them unique (but that smacks of record-keeping -- ha!).
It's important to use really sharp scissors to cut the fabric so that there aren't any little threads hanging off (unless, of course, you like that look.)
As the pieces are cut out, it's helpful to look at the intact picture and figure out which pieces would logically be on top. The pieces that will be underneath need a little "seam allowance" so that there will be some overlap of the pieces. This is for two reasons. First, I don't know what background I'm going to use and I don't want any of it showing through between the pieces. Second, I think it makes the work physically stronger -- as in: not as likely to fall apart. Although with all the thread that I'm going to put on this, it will be plenty sturdy. Of course, it would not be good to have really dark fabric shadowing through the light, so that's something else to consider.
I use a pair of tweezers and my precious porcupine quill (thanks, Beth) to move the pieces into place. Then I tack them together with the point of a hot iron so they don't slide around.