Turkish baths are very old, historic places (some of them exist). Before Turkey; there were Ottoman Empire on these lands. I guess no one have a bath in their private home so people go to "hamam" (Turkish Bath) to clean up!
There is a "tellak" which a person washes you with some kind of massage on "göbek taşı" (a round stone in the middle of hamam).
I guess you saw more on documentary.
There's a lot of baths around, but try to avoid the explicitly tourist ones, which normally feature brochures in English of men and women chilling in the Hammam together. Those will be a lot more expensive- although no doubt will be well explained. Those that cater to an exclusively Turkish crowd might be more difficult to understand, as there are a lot of semi-arcane rules to the Hamam, especially for men. I'm also told that there is a bit of a cruising scene at Hamams, although it's vehemently denied by quite a few turks as well.
Anyway, look around for a Hamam in any area but Sultanahmet- try Kadikoy, Beyoglu, or maybe even for a treat, in Bebek or the surrounding areas. Don't expect to get out for less than 40-70 TL, and make sure that you discuss EXACTLY what you want with the attendants. Each time I've gone, tipping has been expected- plan on tipping your masseuse, the towel person, and anyone who does anything for you. 5-10TL should be enough, but again, be sure you've agreed on the price before you submit to any massaging.