Let me tell you as a non-Japanese, you are unlikely to see an authentic geisha first-hand unless you find yourself the guest of a Japanese businessman with a very fat expense account.
Few aspects of Japanese life are more elusive than the geisha. You might see cheap imitations in expensive night-clubs on Tokyo's Ginza or even a real one being driven post in a limousine on the way to on exclusive party.
It is usually unheard of for them to perform for unescorted foreigners, who are not considered sufficiently versed in Japanese ways to appreciate the finer points of this time-honored institution.
The word geisha means "talented person"—in Kyoto, where I'm from, as befits this old imperial capital, she's more elegantly known as geiko ("talented lady"). She has the sophisticated talents of a singer, dancer, actress, and musician.
A girl is token on in her teens as an apprentice and is carefully trained by older geisha in the traditional arts of entertaining Japanese men who want to spend an evening in an elegant tea-house, away from their wives.
Contrary to popular conception, a geisha is not a glorified prostitute. A genuine geisha has the prestige and admiration accorded to actresses or singers at the top of their profession in the West. Charm and personality are considered more important than physical beauty.
A true geisha is primarily of highly trained professional entertainer, hired on the basis of her charm and skills. Casual affairs with genuine customers almost never happen, as these would sully the geisha's all-important reputation.