It seems a lot of people have questions about how to finish perforated paper, so I decided to share the way I do it. I think the most common method is to attach the stitched piece to the backing material (paper, felt, etc.) and then cut it out, but I cut it out first as I find I'm able to get a neater cut that way.
For the backing, I like to use a heavy, textured card stock with a nice sheen on one side. It doesn't matter what paper you use, as long as it has enough body to make the finished piece nice and stiff. My mom uses old Christmas cards to back her small perforated paper Santas and it looks really nice.
Now here's where my method is a bit different from the usual way. I cut out my stitched piece first, then lay it on the backing paper and trace around it. If using a backing paper with a right side and a wrong side, make sure to trace the outline on the wrong side of the paper (i.e.. wrong side of stitching laying on wrong side of paper).
Cut out the backing about 1/8" inside the pencil line.
When cut out this way, the backing will be just the right size to cover the stitching on the back but not show from the front.
Smear a very thin layer of glue on the backing (use your finger to make sure it's smooth--no blobs), place it on the back of the stitched piece, then lay it on a flat surface and place a heavy book on it. If you haven't used too much glue, there shouldn't be a risk of it squeezing out, but if you're concerned, just place the finished piece between waxed paper before weighting it down. Leave it until it's dry.
You'll end up with a nice, neat back.