There are a few things to try:
1) First, make sure you have used the correct details from your host to connect to the MySQL database. These are not usually the same credentials you use for FTP or email.
2) Open up the config/conf.php file and ensure that there are no extra spaces or other typos for any of the values.
3) If you still get the error, download this test file, unzip it, and upload the mysql_test.php file to your Director folder. Then load it in a browser, and note the error that you receive. If the error doesn't help you or your host troubleshoot the problem, contact us.