While occasionally girls
were born to geisha
and became geisha themselves, mostly this was avoided. Pregnancy
tended to detract from the popularity of a Geisha, and abortions
Instead, girls were purchased from poor families. . . this provided the family with finances, and the girl with a life that her family was no longer required to support. The price of this purchase was placed against the girl, with the understanding that when/if she became a successful geisha, the house she lived in would absorb her earnings until such time as the debt was repayed.
This is where mizuage became important. Men would bid on the mizuage, and the highest bid won. . . this often meant a substantial amount of money. . . all of which was meant to go towards paying off a young geisha's debt.
If the girl became popular enough, the Mother (who was in charge of everything in the house, or okiya) might adopt the girl in a ceremony that made the girl a true daughter. In this case, everything the girl owned or earned went directly into the house funds, and when the mother died, the girl was installed as the new "mother".
Before a geisha's mizuage, there was a ceremony in which the geisha and her Mizuage Patron (the man who won) would drink sake to bind them together. The reason for this ceremony was that even though the mizuage itself would be over quickly, the man would remain the Mizuage Patron for the rest of his life.
After mizuage had occured, the geisha changed her hairstyle so that instead of a patterned silk band she wore a red silk band at the base of her pincusion bun. . . this way everyone would know that her mizuage had been fulfilled.