Stockings and socks
Choose a yarn that suits the thickness and quality of the socks. Sew vertically over the hole with a blunt needle. Do not tighten the sock material but keep the sock and the material smooth and stretched. Sew fairly tightly. When you see that you have covered the entire hole, start sewing horizontally. Weave every other up and every other down around the seam you just sewed vertically. It becomes like a grid. Be sure to sew past the hole for increased durability.
These socks are knitted with a very fine knit and it can be difficult to stuff these with regular thread. If the hole is small, try the classic trick with a little nail polish.
If a stitch has been missed, you may be lucky and be able to catch it with a crochet hook. Catch the last stitch in the tear with the hook. Then take and pull through the yarn from the next row in the knitting and pull through the stitch. Continue until the tear is gone and carefully fasten with a thread on the back.