I washed my 580 pads by hand a few years ago - one of the worst experiences of my life. Anyways, what I did:
Took two lids from 50pk CD cake boxes, put one with warm water + my laundry detergent (I use dye/perfume free HE detergent, so it also lacks a surfactant), and another with cool rinse water. I just messaged them in the "wash" area for a few minutes, and then rinsed them (which takes multiple cyclings of the water; I think I exchanged it 4-5 times to get them fully clear of the soap (basically go until they don't release anymore soap and the water stays clear)).
Then I patted them dry with a towel to get the "sopping wet" off of them, and set them out to dry. But that wasn't happening fast enough, so I wrapped them in a clean t-shirt, wrapped that in aluminum foil, and put that on the shoe-insert for my dryer, and put the thing on "low" and let it run for ~hour. They were mostly dry by then.
Things I learned:
- Don't rush the rinsing, or you'll leave soap in the pads (which is bad)
- If you're using a dryer, if you have a shoe insert it's a good thing, but still wrap them in something. Don't use "ultra high" heat, as it may damage the plastic.
- Be gentle while washing them by hand, and be especially gentle if you decide to wash the foams (those will air dry, no need for putting them in the dryer).
I would not use shampoo or body wash or triclosan or alcohol based soaps, as they're generally fairly harsh by fabric standards. Laundry detergent is designed for what you want to do, and using the HE stuff will remove the surfactant and make the rinsing easier. Woolite is also a popular suggestion, because it's even milder - it would work, but I don't like going out and buying extra stuff.
I would avoid fabric softener, detergent boosters, etc.