Disc space is full, but can't access desktop to delete/backup data

My computer says my disc space is full, and now I can't even get to the home screen. I've tried restarting several times, but all I can get to is the log-in screen. After I type in my password and hit 'enter' the screen goes blank. The only thing I can do from there is hit the power button to restart or shut down. How can I get to my desktop to move files to an external hard drive and free up some space?