Oh there are tons of video game composers looking for games to make music for!
You can find a whole bunch of them right here on Itch.
I found the composer for my game on Instagram.
So here's basically how the process worked:
First, we worked out the scope of the project. I told him that I needed 5 one-minute tracks that were loopable (meaning that the end of the track seamlessly allows the music to start over). I also told him what my timeline for completion was.
Then we agreed on a price. He even had an invoice that was filled out. Two other conditions he had were:
He wanted his name in the credits (of the same font size and on-screen duration as mine).
He would adjust the music up to 3 times.
If I remember correctly, I paid for half of the music up front and then paid the rest upon completion.
As far as the creative side of it, here are my tips for that:
1) Give them a free demo or copy of your game so they can better see what they're working with. At the very least, send them a link to a playthrough video.
2) Listen to other tracks of theirs and tell them which tracks you like and specifically what parts of those tracks you like. This helps them narrow down the kind of sound you're looking for.
3) Send them samples or links of other tracks you have in mind for different parts of the game. They can use these as inspiration for the original work they'll be making.
4) Tell them what emotions you want the player to feel with each track. If it's a boss fight, should it feel fast and furious or slow and grueling?
After that, just sit back and wait. It's a huge rush to hear original music for your game!
Finally, don't be afraid to ask for edits or adjustments -- especially if you're paying for it! You can usually get them to change things up to 3 times.
If you do ask for edits/adjustments, be specific as to why you want something changed. I remember on one track, I told him that a certain instrument was too prominent at one point and needed to be cut out or lowered in volume. The more specific you are, the better they can fix it for you -- and a lot less grudgingly, too. If you say something like, "This sucks, please fix it," the next edit might be even more unexpected.
Hope this helps!