Many use regular dishwasher liquid, since it's a degreaser and mild.
You want to put your ball in a 5 gallon bucket and put the soap and warm water in there. Some people use hot water, roughly no hotter than 120 degrees F. Basically, it's best to gradually put the water in that high temp. Start first by soaking the ball in warm water. Wait 15-30 minutes or so. Then soak the ball in even warmer water, wait, etc. Until you get to the hot water. You have a high chance of damaging the ball if you just dump it directly in hot water.
You should see an oily film on top of the water. Just dump the water out and repeat with hot water and soap. Repeat until you don't see any more film. It's ok to get the finger holes wet, but some people cover it with something, like putty. I actually don't fill the whole tub completely, but just to the point where the holes do not get filled. Oil should not track in the hand area anyways.
I recently changed my method by just rubbing dish washing liquid on the ball then rinsing it under a faucet. I seem to get similar results and also takes less time.
Regarding a towel, I actually use a micro fiber golf towel. Golf towels usually have a clip, so you can clip it to your bag. I actually clip it to my belt, so I don't have to dig for it.
Hammer 1st Blood 15# (@1500 Polish)
Hammer Taboo 15# (@2000 Polish)
Hammer Taboo Blue/Silver 15# (@4000)
Storm Natural Pearl 15# (@4000)
PAP: 5 3/4 right 1/4 up
Ball Speed: Mid 15-16 (Power Tweener)