Keep current theme active while working on new theme

I’ve looked, but haven’t found the answer to my question.

I need to change the current theme of my site. But I would like to keep the current theme active (online) while I copy and configure my content to the new theme in the background. Then, when I am sure the new theme looks the way I want it to look, my goal would be to simply deactivate the old theme and active the new theme.

How is this accomplished?

Also: what is the purpose of the two additional themes, twentyten and twentyeleven?

Thanks!