This is one way to do multi-layer appliqué.
Step 1: Find an image to use that lends itself to appliqué. Clear big shapes are easiest, coloring pages are good but of course you have to be careful about using someone else's artwork (you cannot sell something based on another's artwork). See how it fits on what you want to put it on. Resize if necessary. I would save it after resizing, in case you need to print a reverse image or if you need to reprint because a little person steals your image for coloring!
Step 2: Get out your scraps or whatever fabric you want to use. Prints can be very cute in appliqué so don't forget to check those. Mixing knits and wovens are fine. I used the back side of sweatshirt fleece to get a more fuzzy look.
Step 3: Fuse Wonder-Under (or Heat 'n Bond) on the back of your scraps. It is easier if you fuse a larger section than you need for the piece(s).
Step 4: Trace your image on to the paper backing, being careful to face your pieces the correct way up. If you are using a thick fabric for the applique, you may want to print a reverse image and trace directly on the paper backing instead of trying to trace through the thick fabric.
Step 5: Cut out all your pieces and arrange them to make the design. At this point you can trim and fiddle with the pieces. I simplified the shape of the nose area as I didn't think it needed the delineated mouth.
Step 6: Fuse the smaller pieces on to the base piece(s) but only do the ones that are completely on the base piece. In this instance I fused everything except for the antler, nose, tail and hooves.
Step 7: Fuse the base piece on to your garment piece or finished garment. Place the rest of the appliqué pieces on and fuse. If necessary, use Wonder Tape or washable glue stick on any difficult parts.
On this particular image I marked the eye and legs where it needed additional stitching inside of the same piece.
Step 8: Stitch around each raw edge. Experiment on a scrap first! A little bit of waviness can be steamed out but you may need to use a stabilizer or a walking foot. Satin stitch/zig zag is traditional but straight stitch is often used (be mindful of any curling edges or fraying of woven edges). Press if necessary.
And that's pretty much it. Finish your garment normally. Thanks for looking and reading!