It depends but in most cases I’ve heard the girl sends an email or just ordinary mail to okiya or ochaya - many of them are now available with their websites and even facebook pages. Some okiya homepages have a specific ‘fill out’ form and FAQ for girls interested to be maiko ( I think it’s interesting to notice how this has changed over the years). For example if you read geiko Komomo’s book you will see she had a correspondence with her okaasan Koito before making the decision to join the okiya.
So to sum it up the first step should be that the girl contacts an establishment within some hanamachi (either okiya or ochaya who will introduce her to some okaasan who is currently accepting apprentices and most okiya are always open to new apprentices). Some okiya will even let younger girls come for a ‘summer trial period’ so that the girl can spend a month or two of her summer break in the okiya to see how it feels and whether she wants to do it or not (this is still not a very popular method but I’ve seen it used in a few okiya). In any case, after the contact has been started okiya will usually request for a photograph, basic information and of course a document that proves the girl’s parents allow her to leave their home (which is why they must be min 15 years old before joining). The kenban comes in at a later time as they mostly deal with the maiko and geiko’s schedules, proceeding payments, renewing their contracts etc (Kenban is basically the accountant and law team of the hanamachi, in a figurative sense of course). I hope this wasn’t all too broad, it’s hard to talk about it without a specific question in mind.