The pattern is very simple, only three pieces: a top side, a lower bottom (with thumb) and an upper bottom (also with thumb). The two under sides get sewn across, making a center palm seam which also encompasses the thumb, giving it free movement. Then the flat underside gets sewn to the upper side, pressed, turned and pressed again.
This looks better with a dark or patterned sweater - the palm seam is very obvious on this light green, but then again, I want it to be obvious so you can see what I'm doing. So there.
Cut the upper side and the lower under side pieces, using the band of the sweater. This will make the cuffs of your mittens. I like to cut them a little longer because I like my mittens to fit snugly up under my sleeves. You may have to adjust the width of your band depending on its stretch; it won't likely be too tight, but it may be too loose and you may have to bring it in. Cut two top sides, which will be identical, and two under sides, which will be left and right.
Press everything so that it's nice and flat. Then pin your two undersides together at the center palm seam, from the base of the thumb across to the inside edge of the hand. Stitch from one side to the other, taking care to give yourself a nice sharp corner where the palm meets the thumb. Trim the seam, zigzag it for security and then press it, on hot, with the seam and the thumb facing up.
Pin the under side to the upper, thumb side facing up. Pin your way around the curve of the mitten until you get to the thumb area. Making sure that the edge of the thumb seam is caught in the side seam, but that the thumb itself is still flexible, pin all the way to the bottom of the band. If you can, gingerly fit your hand inside the inside-out mitten to check the fit of the band. If it needs taking in, it's easier to do it now.
Stitch around the mitten, following your pins. Again, trim the seam and zigzag it, then press it again. Turn the mitten right side out, reshape as needed, and steam it one last time.