I don't use socks any more, but when I did, here was my process:
Two important notes after a year or so of only having two socks and hand washing them when swapping them out. I installed a hose attachment to my basement sink. This sped things up, but it still took a while to get nice and clean. I decided I needed more socks, so every time I went to the LFS, I bought a new sock. Socks aren't expensive, but back then I would have felt buying 10 at once. Once I had 10-15 socks, I used this process:
As soon as the sock is removed, I would turn it inside out and thoroughly rinse it. Takes 2 minutes tops.
Leave inside out, put it into a bucket, it will dry, no worries.
Once all the socks were dirty and rinsed, I put them into the washing machine:
1 cycle using hot water on gentle
1 cycle using warm water on gentle
No soap. I also keep my hot water tank on a pretty high setting.
While still wet (this is important), turn them right-side-in.
Put them somewhere to dry (don't just throw them into a wet).
Once dry, store for later use.
Gentle cycle may not be needed, but I didn't want them to get ripped apart...