The Thumb Trick:
Sometimes called an afterthought thumb, I first read about it in Elizabeth Zimmermann's Knitter's Almanac. I really like this method because it's seamless; sometimes when patterns have you place stitches on a holder and then cast on the top stitches you can get an odd seam right in the crease where your thumb meets the hand, and that can be uncomfortable. The only trouble that some people may have with this method is that you cannot immediately try on your mitten in progress, as you can with mittens where the stitches are put on holders. But if you want to you can just knit a few more rows and then pick up the stitches instead of waiting until the mitten is done, threading the waste yarn through them so you can try on your mittens as you knit. The trick: Knit to where you want to place the thumb hole, and take a length of contrasting yarn, and knit the thumbhole stitches with it instead of your working yarn: (see the working yarn, still on the right-hand side of the work?) Ta da!
Related: Knitting and Crochet Techniques