Cut the character out with about a half inch of space all around it. To make a back that matches, outline your pre-cut character onto whatever material you wish to use for the back and cut it out (the example I made came from a two-sided shirt, so they just happened to have a cool backing already).
You're already halfway there.
Next take the two pieces, lay them down in an inside-out manner (facing inward, and sew roughly all along the edges until you've sewn the entire circumference, leaving about a 1.5 - 2 inch opening.
Next, pull the material and flip the little guy right side out so you can now see him, and he's flat.
Fill it with beans or soft stuffing or even sawdust.
Then sew up the gap. And you're done!