I think mending is best taught sitting along side one another, and then practiced, practiced, practiced. And you can totally teach yourself, too.
My objective with mending is first to get the thing back in circulation. In use is better than perfect. Perfect can be figured out later. It’s better to be wearing that sock again, even if your darning a little wonky. Your stitching gets better as you go. Utility and beauty. But first, utility.
In general, there are two main ways of textile mendings: Darning and Patching. On my beloved old LLBean sweater, you can see both. The navy block is a patch– whole cloth where the edges are turned under and stitched on top of the fraying knit. The white stitching are types of darning, Swiss darning to be precise.
I’ll post some more tutorials soon, but for beginners, I always start with the stocking darn. It’s quick and pretty easy. Start with a sock. Wool is best. Look for a hole or a worn spot to reinforce.
Curiously, Patagonia has some pretty good tutorials on their website for mending all sorts of things. https://www.patagonia.com/worn-wear-repairs/