Fix a Hole or a Snag
You can mend your sweater to make it look as good as new, whether you've torn a hole in it or just snagged a small portion of it. If you have a small snag in your sweater, but the threads are still intact, you can repair the snag with a needle-threader.
Push the small wire on the threader through the snagged part of the sweater from back to front. Pull the snagged threads of the sweater into the wire loop on the threader, then pull the threader out of the sweater. As you pull the threader out, it should reposition the threads so that the snag disappears.
You can fix a hole in a sweater by trying to recreate the knit of the sweater. It's easiest to repair a small, one row hole, but you can fix a large hole as well. To repair a hole, thread a thin needle with yarn that matches your sweater. Open the hole wide enough that you can see the loops of yarn on the top and bottom of the hole.
Push your needle through the yarn loop on the top of the hole, then into the loop directly below it on the bottom. Bring the needle back up to the top of the hole, pushing it through the next loop. Continue stitching through the loops until the hole is concealed by the yarn.