When you go to a public bath, bring your own soap, shampoo, small towel and regular towel for drying off. If you don't have essential items, they're often for sale at the bath.
Pay the entrance fee, put your shoes in the designated spot and go in the separate entrance for men or women. Take off your clothes in the changing room, and put them in a locker or a basket. At this point, many people cover their private areas with their small towel.
Pick up a bowl and a stool, and head for the faucets lined up on the wall. Sit on the stool, fill your bowl with water and pour it over you. Soap up thoroughly, wash your hair and keep rinsing with bowls of water until you're squeaky clean.
Head to the bath, once again using your little towel for the sake of modesty. Enter the bath very slowly--there's really no other way because it's excruciatingly hot. Enjoy a wonderful soak as long as you can stand it.
Get out of the water, rinse and dry off, go home and pat yourself on the back for enjoying a unique cultural experience.