Installing wordpress – building a site – then moving it all to existing domain

Hi,

I wondered if anyone could tell me the best way to build a wordpress website and put it on a sort of ‘testing’ domain and then move it to a pre-existing/purchased domain.

I am building a website for someone who already has a site, when the new website is built I need to transfer the site over to the existing domain name.

I have had a good look on google, but I have a feeling that I am just not using the correct terms.

I normally just buy a domain and install a version of wordpress and then start building.

Any advice would be much appreciated

Thanks