How to design new wordpress with old in place?

Hello,

The situation:
I’ve been given the project of redesigning a clients website. The current website is WP which is great, because that is exactly what I wanted to work on. The old website isn’t anything like what I want the new version to be so I’m going to start from scratch.

The question: How can I design my new wordpress site while keeping the old one in its place until I’m redo to switch the two. Do I install it in a root folder or something?

If I do that will I be able to keep the current theme in tact while I’m working on the other one? The project will probably take me a month or two and I don’t want the website to be blank for that time.

I’m sure this is a really simple problem to solve for most, but I’m a print graphic designer more than I am a web designer.

I’d be extremely grateful if you threw me some links or a brief explanation of what is the best way to do this.

Also, I’d like to transfer the previous blog database info over to the new site when it is ready. So I don’t know if there is a better way to handle all of that to make the database transfer easier.

Cheers