This is the best stitch I've learned for puppet making. When done right it is virtually invisible, allowing you to have seams in seemingly unsightly places. This comes in handy especially if you are creating a puppet with an unusual shape. Here is how it's done.
1) Anchor the thread at the start of the cut with a secure knot.
2) Starting to the left of the cut, thread your needle in and out about a quarter of an inch from the cut. This stitch should run parallel to the cut.
3) Bring the needle to the right side of the cut and parallel to the in point of your first stitch. Thread it in and out about a quarter of an inch from the cut, creating a parallel stitch. You should now have two stitches that are side by side.
4) Bring your needle to the out point of your first stitch on the left of the cut and thread it in and out just as before.
4) Bring the needle to the right side of the cut and parallel to the in point of your second stitch. Thread it in and out, creating another parallel stitch
5) Continue in this fashion until the whole cut is sewn up.
Essentially this stitch is pulling together the two sides of the fabric while burying the cut ends.