Install and build a site offline

Hey,
I am fairly new at this wordpress thing, just built my first site with it last week.

I want to build a brand new site for someone else using WP. Their domain has a fully operational website on it (it was built with FrontPage by someone else). They want don’t want the current site to go down until the WP site is ready (using the same domain).

Is there a way to build and test my WP site on my desktop, so I can show them the new look and changes (for approval). Then upload it to the domain and replace the old site?

I am hoping that there is some kind of program that simulates an SQL DB on the desktop to get it done. Any ideas will be appreciated.

Thanks in advance