The scrap yarn acts as a stitch holder and keeps the unworked stitches out of the way as you just work each finger. You will then take a few stitches off the waste yarn and work each finger in turn. The easiest way to put these stitches on a piece of waste yarn is to thread a yarn needle and insert it into each stitch, sliding it off the needle. A contrast color will make it easier to see.
Knitting these short fingers on fingerless gloves is a bit intimidating for some beginners and intermediates. If you absolutely can't get it, you can knit a ribbing 3/4 of an inch from where you want the glove to fall and bind off with a regular bind off. The regular bind off will make the gloves a little snugger around your knuckles. If you finish the gloves off with a ribbing rather than fingers, the distance from the thumb opening to the finished top of the rib will be 1 3/4 to 2 inches, depending on how long your hands are. That's an inch of stockinette stitch and 3/4 inch of ribbing. Or for two inches, 1 1/4 inches of stockinette and 3/4 ribbing.
I can knit fingers on gloves, but I just don't have a lot of time lately with working. I've switched from doing fancy fingers to the simple but functional ribbing.