I'm not a guru and I'm not sure if this will work for you too, but I did the following and that worked for me, creating my own theme, based on twenty ten:
With ftp I got the directory wp-content/themes/twentyten down to my computer.
I renamed the directory there to my theme name. In all the files inside I 'find and replace'd all twentyten to my theme name, as well as all Twenty Ten and Twenty_Ten.
In the stylesheet I also edited the description of the theme and the author.
Then, when I was sure there wasn't any twenty ten left in the content any more I uploaded my theme directory with ftp up to wp-content/themes/mythemename.
Then it was visible in the backend (i believe it's called) in appearence/themes. I simple activated the theme. The only things that were missing were the background and header image. Rest functions completely.
Hope this works for you too. Good luck!