I've never had to purchase hosting for a PHP/MySQL environment before. Usually I just need .NET hosting by itself. If I've ever had a sql backend I usually hosted it myself. How would I setup the MySQL hosting (such as hostname, credentials in my config)?
I'm assuming they provide this information?
It depends on your hosting provider/setup.
You can create databases and setup user/pass on your own if you've got a control panel.
When you buy LAMP shared hosting, they just create a control panel account (typically CPANEL) for you.
Form here, in case of cPanel, you can create MySQL database, users and set their passwords. Typically there is phpMyAdmin software installed to access your MySQL databases over Internet.
Few providers create one MySQL database for you and share credential details with you. They have different databases for each customer.