How to work on theme without being live

[jtaylor]

I know this is probably one of the most basic and simplistic questions, however, I can't find the answer.

I setup studiopress on my site a few months ago, however, I have learned a little more about web design since then and want to redesign it. How do I go about redesigning a website without the changes showing up as I go.

Also, I now have someone who wants me to design a website for them which I am excited about. However, I am not sure how to design again without it being live.

I hope this is the right place to ask this because I am completely stumped. Thank you for any help you can give!