Okay sock knitters and enjoyers of hand knit socks (or just any socks, in general), I did the research for you, and it turns out that it's not too hard to darn your socks.
There are several different techniques, and I tried out three different ones. There's the (1) Swiss darning (or duplicate stitch) method, the (2) running-stitch-weaving method, and then there's the (3) knitted patch.
I found some pretty good videos from Knit Picks for the first and third methods (see below), and there are a lot of advocates for the woven method (but not many good videos). It's certainly the easiest, and for machine made socks, it's probably the way to go.
The first sock had a fairly small hole, it appeared that it was mostly just the yarn between two columns of stitches that was broken, so I used Swiss darning to close it up. This basically means that you duplicate stitch over the area to be mended. It really works best for strengthening thin areas, not so much for closing up large holes, unless you want to build up a framework with heavy thread, which is later removed. I have to admit, I went a little cross-eyed trying to stitch everything in the right places because my socks were somewhat felted in that area. Still, the beginning of a greater disaster has been averted, and while it may not be pretty, it is definitely functional. I also didn't have matching yarn for this sock, but what I used blends well enough. Here's the part one video (you should be able to click part two when it's done):
For sock number two, I did have matching yarn. The hole was more like two holes, and pretty big. I used the regular old weaving method for this one. I am interested to see how strong it will be. It isn't super pretty, but it's better than a hole, and I'm glad I could match the yarn. It just blends right in. It's nice to see that Lorna's Laces really holds its color. This was about the best video I could find on the weaving method (I really wove my stitches, going over and under on opposite rows, this looks like just a bunch of random stitching to me):
The knitted patch is good for larger holes, and it wasn't too hard to do. As you can see in my picture above, the Malabrigo yarn has faded quite a lot from washing and wearing. It's so nice and soft, but I'm not sure I'll use if for socks again. I am a little concerned that the patch will feel like a huge lump when I wear them. I tried them on, and I can feel it, but it's not too bad. We'll see if it's bothersome after a whole day, though! I do like how nice and tidy it appears. Again, it's a two-part video, here's the first part:
There are some advocates for just sewing a hole closed, but that seems like a bad idea, especially on the bottom of your foot where you would feel a big lump. So don't do that! Has anyone else darned socks before? What method did you use? I'm so happy to have my socks back! My feet will now be warm for the rest of the winter.