I don't know how to "darn" socks to fix a hole. Perhaps some day I should learn. In the meantime, I found another use for those socks...they become rags!
It's so simple to do! First, make sure the socks are clean. (Some people prefer to bleach socks before repurposing them.) Once they're clean, cut them in half in a straight line until they're open...like a rag. (I don't have any pics this time because we didn't have any socks ready for a sacrifice.)
They'll have rough (i.e.-non-pretty) edges. If you're so inclined, you can hand or machine sew these edges to make them pretty. Honestly, though, I'm using an old sock with holes as a rag.
My favorite "rag" socks are the thick men's socks. I use the inside of the sock as my cleaning side. It provides a "scrubbing" surface of sorts.
What do you repurpose?