Hold you hand out for a minute. See how the base of your thumb goes out above your wrist? That's where the mitten gets bigger than those original 38 stitches. You pick the spot, set aside two stitches, and increase until you have 14 stitches between the markers.. (ummm...I think that would leave you with 50 total, but do your own counting 'cause I'm half awake :D) When you have 14 stitches between the markers, you'll put them on a stitch holder (big safety pin, chunk of yarn, whatever) and keep knitting the body of the hand on the...ummm...36 stitches or whatever that are left. Like she said, start on a mitten and you'll get it.
OH! Your "buttonhole" idea? Yeah, that's on the right track. You leave the stitches live on the stitch holder and work around them.