I had a pretty decent idea of what that would entail, but I still looked to the internet for guidance. I learned that a lot of people call it darning when they just sew the hole in the sock shut by pulling either side together. I think that's a questionable choice when it comes to socks. First off, it'll result in misshapen socks. On top of that, it introduces a seam to a high-wear area. Seams in socks aren't comfortable anywhere, let alone right at the heel. What I wanted to do was to reweave the area that was missing and fully integrate it into the surrounding fabric.
I started out with a sock that had almost worn through. I could've waited for it to really be a hole, but this worked too.
I stretched it over a glass jar because I don't have a darning egg. Socks are stretched quite a bit when you wear them, so you want to design and execute your repair in a way that takes that into consideration, so a darning egg or a jar or whatever will keep it appropriately stretched while you work.
The first step is to grab a darning needle and some wool yarn that is around the same thickness as the stuff the sock is made of and stitch a big square around the hole. Don't knot the end of the yarn. You want it to be big enough to include a decent section of intact fabric on all sides of the hole. From there you stitch columns up and down all the way across the square. Next, you stitch the rows. When you reach the area over the hole, it'll be covered in a bunch of vertical threads from having done the columns. You want to weave your rows through, over-under-over-under (then, for the next row, under-over-under-over, etc. etc. ad nauseam). This creates a woven fabric that fills out the hole.
When you're done, do a few extra stitches around the edge and cut the yarn without knotting it. The extra stitches will guard against your thread pulling out from the patch. You would be able to feel a knot, and that would be unpleasant, so they're best avoided. Because it's wool, it will with use felt together and otherwise cling to itself to form a cohesive fabric. Just be sure to wash it on cold and hang dry. All fixed!

