I begin the thumb by putting the stitches on the outside of the thumb back on the needles. I take the waste yarn off after I put the stitches back on the needles. The waste yarn usually pulls right out with no problem and it is even more likely if I've taken the effort to find yarn that is a lighter weight for the waste yarn.
I knit across the front stitches in pattern. Here I'm using a contrast yarn in pink to try to show this process better. BTW, notice the sharp Knitpicks' metal dpns - for picking up stitches, sharper is better. I always use needles to pick up stitches (I insert the dpn through the location where I want to add a stitch, then knit a stitch onto the needle.) but you can use crochet hooks as well.
When I get to the side of the thumb hole I am going to pick up a stitch on the side of the thumb as the pattern states to do. (I never pick up more stitches than the pattern specifies around a thumb or finger hole - I think it is noticeable and I prefer to use the reverse duplicate stitch to fix any loose stitches or holes after I'm done knitting.) On the side of the thumb hole between the stitches knit from the waste yarn and the cast on stitches on the back there are two stitches - a yellow green and a darker green. I pick up a stitch through one of these two stitches. If you look at both side stitches, the yellow green stitch is a bit looser. That is why I decide to pick up the stitch through the dark green stitch. (Picking up stitches through loose or large stitches often seems to make them more noticeable, not less.) I just pick up a stitch through the right side of that darker green stitch.
They're all on the needles now.
Next post - picking up the sts from the cast on edge.