So the question is what is this mysql database? is it empty and you want to store your SilverStripe site in it? Then simply run the installer on your webserver. The installer will ask for your mysql username, host, password and database name. Once you enter those details and the installer is green then you can install and SilverStripe will write the configs and settings for you.
If the database you want to connect to is an existing database (eg a Wordpress database) then you cannot use that within SilverStripe easily. You will need 1 SilverStripe MySQL database then convert your content from the other one into this one.