Currently, Kyoto is considered, by many, to be where the geisha tradition is strongest. The geisha in these districts are known as Geiko. (The Tokyo hanamachi of Shimbashi, Asakusa and Kagurazaka are also well known.)
Geisha are often hired to attend parties and gatherings, traditionally at ochaya (お茶屋, "tea houses") or at traditional Japanese restaurants (ryōtei).
Being a Geisha was widely practiced throughout Japan's history. In the 1920's, there were around 80,000, beginning from when a child was around the age of 4. Nowadays, it is a rarity to see one, and most choose the lifestyle as adults.
You will most likely need to be in the specific areas where it is still practiced in order to see them, their numbers ranging from around 1,000-2,000 total.
Modern geishas still live in traditional geisha houses called "okiya" in areas called Hanamachi (花街 "flower towns"), particularly during their apprenticeship. Those studying to become full geishas are called Maiko. Many experienced geisha are successful enough to choose to live independently. The elegant, high-culture world that geisha are a part of is called karyūkai (花柳界 "the flower and willow world").
Geisha still study traditional instruments: the shamisen, shakuhachi, and drums, as well as learning games, traditional songs, calligraphy, Japanese traditional dances, tea ceremony, literature, and poetry.
Opportunities for tourists to dress up as Geisha in traditional kimonos with painted faces is widely available and enjoyed for a small fee.