...or if you'd like to just work on the CSS format/layout locally, that's very possible also. (Maybe I'm stating the obvoious here.)
Grab the source of your page and save it locally. Also save your wp-layout.css locally. Now, make sure the page source actually points to the css file. The import statement of the default setup still points to your online style sheet.
Now edit your local css file to your hearts content, and view the file locally in your browser.
My host is a bit slow (I'm a cheapo) so this proved a lot faster.
And if you want to do it online, just save your index.php and wp-layout.css with new names, on your server (this should work, shouldn't it?). Then experiment all you want.
Not very hidden to prying eyes, but your changes won't affect the current look until you're ready to switch over.