Silly Beginner Question

Hi. I’ve just getting to grips with building my own wordpress sites and really enjoying wordpress, my test site is beginning to look just as I want it to.

This is more of a hosting/redirection question.

I have built my test website on http://examplesubdomain.mytestdomainname.com

My actuall website is currently http://www.thegreenwoodtreegallery.com/

My new lovely wordpress site is almost ready to go live but how do i point the domain address at my test site? I don’t want to do just a simple 301 redirect of the domain, because then it just shows my http://examplesubdomain.mytestdomainname.com in the address bar.

Do I need to actually rebuild (exporting all my wordpress files etc) onto my domain? Or can I just point my preferred domain name at the location is has been built and keep the domain name in the address bar, along with the subfolders?

Does that make sense?

I set up and own all the domain accounts etc.

How do professional web design companies manage to flick over a new site from ‘old site’ to ‘new site’ without needing to take down the domain name and rebuilding on the preferred domain name?