You'll need a large piece (as large as your child) of fabric that's white or beige, or tan, or pink, or any color you can label with markers. We used some old bed sheets. Double up the fabric and try to smooth all the wrinkles out of it, so you have a front and back for your flat kid. Have your child lie down on the fabric and position his arms and legs kind of like a paper doll. Then draw around him, leaving lots of extra room. Make the head bigger and rounder, and don't make the crotch come to a point -- make it more of a gentle arc. :)
Cut out on the line, or have your child cut it out if he's adept with the fabric scissors. Then sew it up, leaving a space at the waist for turning and stuffing. Clip the seam allowance at the curves and trim around the points so it looks smooth when you turn and stuff. Then... you guessed it... turn and stuff! :)
When you've stuffed it (you'll need about one bag of stuffing for each foot your child is tall), stitch up the hole at the waist. At this point I put faces on ours, so they didn't look so creepy (to me). You could also add hair -- I am meaning to do this but haven't yet. Get out the Sharpies! It's time for permanent marker fun! Wheeee!!!
My two-year-old daughter did not want to label hers, so we left her dressed and she sleeps in Sadie's bed with her. My son, however, was eager to label "Flat Benny" with all his parts, so we did one side the skeletal system and one side everything else we've learned so far (digestive, respiratory, circulatory, etc).
Now Benny sleeps with his flat Benny too! Kind of like a body pillow but educational, and with a urinary tract drawn in excruitiating detail. :)
Check it out, Boy+ Academy did this project too!