When I try to install MODx, I get a message telling me that the connection to the database failed. What does that mean?

First, you need to create an empty database for MODx to use. Usually this is done using PhpMyAdmin. If you are installing MODx on your local machine, you can usually run it with http://localhost/phpmyadmin, if on a remote host, look for it on your control panel. If you have already created the database, check your config.inc.php file in the manager/includes directory to make sure the settings for the database at the top of that file are correct.