Creating a new version of a site

Off the bat I’m not positive I’m posting this to the correct forum.

A family member has asked me to overhaul their companies website. I’ve done updates to their website in the past but not changes of this magnitude.

That being said I’m relatively new to webdesign. I do have a some formal training in graphic design, layout, copy editing, and writing java script; as well as real world training with wordpress.

Now that I covered the background my issue is that I want the original site to stay in place until the new one is completed and I am unsure what is the best way to go about this.

Any assistance is much appreciated.