Please help. Looking for the correct procedure for setting up domain mapping?

Hi is it possible to get a breakdown / overview of all that needs to be done to map a domain i.e. http://www.mycooldomain.com -> subdomainof.websitesintraining.com

But so that it still looks like http://www.mycooldomain.com

Am lost with it all, my hosting is on hostgator, have setup wmpu domain mapping plugin, configured everything or so I think I have, but I did a test and the only thing it does at the moment is send test.websiteintraining.com to controlwordpress.com*

*which I am aware is not allowed by wordpress... bought it before realising, just using for test purposes then releasing.

Thanks in advance for any guidance, just there are a lot of guides out there and none seem to provide the complete picture.

Cheers, L