Working behind-the-scenes/basic question

Hi all. I have a basic page up right now using the 2012 theme.

marcblaustein.com

I am interested in possibly buying Pexeto’s Story theme. I’d like to have my current page up while developing the new site, then switch over without any interruption.

I’m sure this is a very basic issue but I don’t know how to do it. Please advise.

Thank you!