First stretch the hole over one hand by putting it inside the sock.
Taking your thread, start on one side of the hole, and make the first stitch.
Pull the thread through, and leave a tail of about one inch. Push it through to the back for later.
Next, start to build up a structure by sewing lines horizontally along the hole, to start a sort of web.
Next, make perpendicular stitches, going over and under the horizontal ones forming a woven fabric. Every time you double back do the opposite to the row before.
Lastly, make a final stitch and bring the needle and thread through to the back.
Tie a knot between the start and finish, and trim the ends.