Geisha and trainees usually belong to okiya houses where many of them live and prepare for work. There are two basic types of geisha. One is called tachikata who mainly do traditional Japanese dance (mai). The other is called jikata who mainly sing or play instruments.
Geisha districts are called hanamachi or kagai. In Kyoto, there are five hanamachi. Well-known geisha districts are also located in Kanazawa, Atami-city, Niigata-city, and several areas in Tokyo, such as Asakusa and Kagurazaka.
There are usually ochaya in geisha districts. They are a sort of banquet houses which rent rooms for parties where geisha entertain customers. Ochaya are small Japanese-style houses with wooden doors, tatami floors, and so on.
Having a party in ochaya or inviting geisha to entertain at Japanese ryotei (high-class traditional Japanese restaurants) have been considered as pleasures for rich and high class people. The cost for a party with geisha varies depending on the number of geisha, food, drink, hours, and so on.
For tourists or first-timers, it's not impossible to have a party with geisha. Well-known Japanese inns, hotels, or restaurants in the cities that have geisha districts might be able to arrange geisha parties for their customers. Try to make an inquiry to hotels you are staying. Also, tours which include dinner or lunch with geisha are often conducted. Please contact Japanese travel agencies. To see gorgeous performances of geisha, visiting one of geisha shows, such as Miyako Odori in Kyoto is a good idea.
If you are going to Kyoto, there are many shops that offer services to get you dressed up like geisha and to take some photographs. It's a popular attraction among travelers.