Was there a set building (if so, what was it called), or did people contact captains directly? Was it common for certain people to just hire an entire ship and crew? How common was the hiring of unsanctioned vessels, such as pirate ships?
It might be helpful if you could clarify where you're talking about. The answer for how to book passage on a ship in ~1500 is going to be very different in Japan, Istanbul, Livorno, and London.