Suddenly the production system has gone to hell. It has destroyed output files, GUIs are crashing, the database is corrupt, unexplainable answers are coming out. The users are in a panic. The sky is falling. And you're on production support.
Rule Number One
Always act calm. You don't have to be calm, but if you act calm, people will assume you have a clue and they will start listening instead of screaming. The quiet will do you good.
Now then, organize your work:
Write each issue on a separate card. Put down what you know, a little of what you suspect, a little of what you would like to know.
Rate each card for urgency, how soon must it be addressed, and importance, how big a problem is it if it isn't addressed.
Work on one card at a time, most urgent first. Finish one, go to the next. Repeat until the sky doesn't fall after all.
Keep the user informed, even if you dont have any new progress to report, the user likes to know that someone is still paying attention and that they havent fallen thru the cracks. The higher the severity-level of the crisis, the more important this seems to be, and the more frequent the communication needs to be to keep the customer calm.
Stay in control, if the customer is wanting conference calls with the whole team every 30 minutes, not much is going to get done; appoint someone to speak for the team at those meetings so that the team can continue to work.
Sometimes there's so much to do that you need help. Now that you have all these nice cards with the facts, suspicions, and questions, and now that you have them rated, call the team together and get them to take cards and work on them. If you need more help, the cards should provide all the BusinessCase you need to get it.
Often, you'll find that most of the things you are worrying about aren't that big a deal and you needn't feel all stressed. Turns out that acting calm can make you calm after all ...
Then hold a PostMortem.