When my users login they see the WordPress Admin Bar across the top of the page, the one that says, "Howdy, [username]". How would I remove that so they don't see the Admin Bar?

You can add the following snippet of PHP code to your theme's functions.php file. This code will check if the current user has access to manage options on your site (i.e., someone like the Administrator) and if they don't have those permissions, it will disable the Admin Bar:

if (!current_user_can('manage_options'))

If you simply want to disable the Admin Bar for all users, you can add the following PHP code to your theme's functions.php file:

add_filter('show_admin_bar', '__return_false');

For more information, see the WordPress Codex page for show_admin_bar().