I've put the stitches from waste yarn back onto dpns. To pick up stitches on the other side of the thumb hole, I take a dpn and insert it into the right side of each stitch directly above the cast on edge. Sorry I couldn't get a better photo of this. Don't pick up the stitches too far above the cast on edge or you'll get too much bulk inside the thumb.
All the stitches are picked up EXCEPT for any stitches that are picked up on the sides of the hole.
Here I am picking up and knitting only one stitch along the edge of the thumb hole. The tendency is to pick up lots and lots of stitches near a hole but this always ends up looking bad even if you go ahead and decrease them on the next row. I prefer to pick up the minimal amount of stitches and deal with any looseness or holes by using my favorite reverse duplicate stitch on the inside of the mitten.
All done. Again the pattern is Chapter 5, Pattern 9 from Anna Zilboorg's out-of-print book Magnificent Mittens.
And a side view.