How to manually transfer files from disk utility?

Hello,

I'm hoping someone from the community can help me out.

How can I manually copy files from my Macintosh HD to an external hard drive? Is there way to open a Finder Window to drag and drop? Or do I have to do this in terminal? I would like to do this at home since it would have taken hours to copy a large file at the Genius Bar.

Problem: I'm having startup issues with my macbook and am unable to boot. The computer is stuck on the grey screen with apple logo. I've taken it in to the Genius Bar and they diagnosed a B-Tree error that is unfixable. Their solution was to boot into Triage mode, have me manually copy my files to an external hard drive, then reinstall the OS.

I note that when I go in to "Open Disk Image", it opens a window where I can browse my Macintosh HD > Users > personalfolder, but I am hoping to be able to drag and drop from this window.

I am running 10.7.

Thanks