If in doubt, use the good old 'LAST'
Listen Acknowledge Solve Time-frame
Let them rant, acknowledge they are upset and what has happened (clarify anything you're unsure of) let them know what you are going to do to solve the problem, (if anything can be done) what THEY have to do, and the time frame you expect a result in/will let them know more...
If they get rude I just say "Being rude isn't going to help, I do a better job with encouragement rather than being sworn at'