I trace each piece of the applique on lightweight fusible interfacing (Wonder Under) then iron the fusible to the fabric then cut each piece out.
Next on the picture of the total applique I number each piece starting with the one that is "on the bottom of the pile" (not necessarily the piece at the bottom of the picture), numbering each one as it layers on top of the one before it. For these snowmen #1 would be the bottom of the snowman, #2 the middle of the snowman, etc with the mouth & nose & being last. You cn number the individual pieces too if that helps.
Then I iron #1 to the background & sew around it with zigzag or satin stitch - but I don't stitch on the parts that will be overlapped by the next piece (this would be the topmost part of the snowman bottom piece). Then I iron on #2, stitch, then #3 and on & on.
Hope this helps.