It's a simple thing but does take a little time, especially for bigger holes. It's best to do the repair before you actual break all the threads but I sometimes let it go long enough that it's too late. A stitch in time, saves 9, as the saying goes...and it's true. I have never had to redarn an area so it is very strong. Darning is basically weaving the new thread into the old fabric.
This time, I had let it go way too long. I had one foot with a completely broken through hole and the other foot had a broken through hole and a smaller threadbare hole.
To do this, you need thread that matches the size of the yarn used...so wool socks will need thicker thread and these tights. I use cross stitching floss. You also need a basic needle and a darning egg of some sort. I use an old lightbulb which is just about perfect. (If you look closely at the bulb, you can actually see where I've used it in the past.) I have this one tucked in my sewing basket since we no longer use these lightbulbs. And of course, you'll need you holey tights.
Slip the lightbulb into the toe you need to work on and slightly stretch the toe around it. This makes it easier to work on. The needle will glide on the lightbulb without catching other threads as well as help to keep the original shape of the toe.
You don't ever want to make a knot because it would irritate your foot, especially if you're repairing the bottom part. Use only one strand. Leaving a short bit of tail, make a running stitch all the way around your hole. When you get back to the beginning, start making stitches from top to bottom, bottom to top, and repeat until you reach the other side of the hole. You don't want to cinch the two sides together so leave them slightly loose. Try to leave the hole exactly the same size as it was when you started.
In this picture below, I just finished the top to bottom stitches and am now ready to begin weaving.
One thread on top, one on bottom, repeating until you reach the other side. Repeat back and forth until you have finished. You'll finish it up by doing one more running stitch around the hole and snip the thread, leaving a bit of a tail.
I realize this is an awful pic but it was the best I was able to come up with. The top hole is the threadbare one I haven't touched yet. The one in the shadow is the one I just darned. It's just to show you the weaving proccess but I actually fill it in much more desely than that.
This is what it looks like when I have finished with the dense darning in each hole. You can see the whole area I have had to darn over the last 8 years...the area with no white peeking through. As it stretches a bit, the little tails disappear.