They're over selling a bit too much

Well go into your control panel, and go to phpMyAdmin and along the left panel you should see the databases that currently exist, make sure your database is there.

If so... on the main page you should see something like this

That's your username, and hostname...

Now From the menu under 'create new database'

Select the option 'privelages' and it will show you all the usernames with access to that database, and what they can/can't do.

You might need to change your global privelages to 'all privelages' (or to the correct privelages for what you need) and make sure theres a password.

So now you should know your host, username, password and don't forget to check the database exists and not it's name ( i think it's all case sensetive bit i'm not sure, avoid using uppercase to be safe).

And then enter the relevant names into your php code.

Even webhosts generally use 'localhost' (very few don't), some may have an i.p address or another name for it.

Hopefully that should help, if not just post