That's kind of an open ended question. It could be as simple as having a composer of your choosing visit you, ask for a commission, settle on a fee, and wait for the goods.

But you may have a particular theme in mind. Maybe you recently read a book or saw a play that you liked that you want made into an opera. Maybe you're very pious and want a morality tale, or you're subversive and want something anti-establishment. Maybe you're the Emperor and want to promote German-language opera over the more common Italian. You can put any kind of requests or stipulations into your commission, as long as you can find a composer who's willing to do it.

Actually, it's very much the same now. I've worked on new commissions, and often it's a matter of saying "I'm looking for a work for X instrumentation of Y duration on Z theme" and they quote you a price and an amount of time.