First, start off your thread with a know on the back of the sweater. Thread the needle through to the right side.
Next, using stitches as small as possible, sew around the border of the hole (still on the right side of the sweater).
Next, you are going to make a series of large stitches back and forth across the diameter of the hole.
Next, perpendicular to the stitches that you just made, weave your needle over and under in a basketweave style, and thread through the opposite side of the hole as if you were sewing another small stitch. Then bring the needle across the other way, first under and then over (the opposite of the way that you wove the previous stitch.)
Continue this under all the the spaces have been filled in. Tie a knot in the back of the sweater. You're done!