Most of this information can be found here, but I’d like to rewrite it for increased clarity and to add a few details. First some definitions:

• umbrella domain: the domain which houses the mu installation.
• other domain: the domain which will have a single WordPress site within the network.

How To

1. At the domain registrar, point the other domain to same nameserver as umbrella domain.
2. In WHM, go to Edit DNS Zone. For the umbrella domain, create a catch-all record:

3. In cPanel for umbrella domain, add the other domain as a “Parked” or “Alias” domain. No redirection.
4. In umbrella domain, install the WordPress MU Domain Mapping plugin. You can install the plugin like normal. Alternatively, you can just put the domain_mapping.php file in the mu-plugins folder, which probably makes more sense.
5. Find the file sunrise.php in that plugin’s directory and move it to the wp-content directory.
6. In the wp-config.php add the line define( ‘SUNRISE’, ‘on’ ); towards the end.
7. In the network settings, go to Settings > Domain Mapping and enable “Permanent redirect”. Leave the others disabled.
8. Create a new networked site which will map to the other domain. Get the id of that site hint: look at the url bar.  (I have gotten some errors at this point about a file not existing, but the site is still created, and everything still works correctly).
9. Go to Settings > Domains, enter the site id and domain name (without the protocol (http://) works fine).

That’s it. Give your DNS records some time to propagate, and you should be good to roll!