Installation procedure for new site with template

I am assisting my sister in getting a new website up and running with a WordPress Theme. I must admit up front I know very little about WP – my experience is with Dreamweaver and iWeb.
Here is the rundown.
She has an existing domain hosted by Bluehost. That is not going to change.
She has a different domain for WP blogging that needs to stay completely separate from the domain on Bluehost.
She has purchased a Theme for the new WP site.
Bluehost is aware of the switch to WP and has “configured” her site to be ready to accept it. We have all the login and user names and passwords @ Bluehost to do the upload when the site is ready.

The hitch is how in tarnation do you build the site remotely and then prep it for upload? Whenever she logs into her account @ WP and tries to access the template it goes to the existing WP blog which we want to leave alone.

Is there a step-by-step instruction page somewhere that describes how to build a WP Theme site within these parameters?
Many thanks in advance.