Installing WordPress on a domain with an existing site

[Moderator Note: Topic title modified. When you start a new topic, use a good topic title. “How do I…” is not a good topic title.]

Hi, my work have asked me to create a new website using a paid for template. My question is how do I work on the new website whilst the old one is still working. As I have used wordpress in the past I know that I have to type in the URL of where the website will be installed. Does this mean that as I edit and publish that the new website will be live straight away or is there a way that I can have the old one run whilst working on the new site.

Thanks,

Craig.