Kuriboh Man,
I can tell you the stitches but I will have to spend some time looking for a link to explain. Hand sewing is NOT my favorite part (when I was in Fashion, I paid to get someone else to do it for me!)
The stitches have to be small and close together to be truely hidden. If you dyed your puppet it may be worth your while to dye the thread. Upholstery thread is the strongest!.
That being said, use a WHIP stitch or a (sorry, I have an upset child) I can't think of the proper name, but it looks like the stitches on a football or baseball.
Sorry I don't have time (right now) to do the investing to find a good explanation. Hope this is enough to get you started.
Remember to take the stitches far enough in from the edge so the thread won't cut into the foam/fleece and pull out. Keep the tension fairly tight, but not so tight it rips out.
P