Keep yourself calm
The first rule of helping another person through frazzled nerves is to make sure you keep calm yourself. You need to try and keep your voice low and even-paced, without tell-tale signs of aggravation.
As the raid leader, you set the example for your group. If you let yourself give in to the temptation to nerdrage, you'll certainly drag down the morale of your whole team. By the same token, try and fight off the "Eeyore" syndrome. If you act down and depressed, then surely you'll tank the team's mood also.
The first step in handling the frazzled members of your raid is make sure you keep yourself the most even-tempered member of your group.
Call a bio break
If you sense a member of your raid is starting to lose control of his emotions, call for a bio break immediately. Send the person a private tell and check in on him. Many times, this is all you need to do; it gives a small break in the action and lets everyone breathe.
Of course, if you're calling for a bio break after every boss attempt, your raid at large will eventually notice that there are problems. This is where we start getting into the deeper into management techniques.
Choose your goal
You will need to decide quickly if you're attempting to make the frazzled player feel better or just keep their frazzled nerves from affecting other people. While it would be ideal to always make the person feel better, if you're having a bad stretch of raiding, that might not be possible.
The essential problem here is that frazzled nerves tend to be indicative of other things; the person might have trouble with a learning curve, might not react with the same speed as the rest of your raid, or, heck, might be struggling with feelings of inadequacy.
It's not your job to be a professional counselor (unless you happen to be a professional counselor -- in which case, rock on). Your job is to run your raid and make sure your raid runs well. Help your fellow raid member, but don't try and be a psychologist.
That being said, a simple conversation or three can go a long way toward helping a person get a grip.
Addressing the frazzle
If you're trying to chill someone out, it might help to send them a private tell. You don't have to send a clever statement or anything like that, just simply say, "You sound stressed out. How are you feeling?"
The open-ended question is important as a way of soliciting more information. Hopefully, the frazzled raider will tell you something on which you can take action. If he finds the fight confusing, you can take the time to explain the fight in a more simple way. If he finds all the spell effects confusing, you could recommend turning down the graphics.
Keep the frazzle contained
If you're not able to help stressed raiders chill out, it is necessary for you to try and help them at least keep it contained. This is, admittedly, a lot easier.
First, if someone's freaking out and damaging the raid's calm, it is perfectly okay to straight up tell them that. It's not only okay, it's your best bet. "Dude, you're damaging my calm" will do a lot to help someone realize they're being needlessly stressful.
Second, recommend they remain quiet if they're worked up. You don't have to be rude about it. Tell the person, "Man, you sound really stressed out. If you need, just leave your microphone turned off until you feel better."
If for some reason, the person still won't chill out or won't keep it to themselves, you may find yourself having to separate them from the raid. It's unfortunate, but we're going from the angle that the person's stress is so severe it's affecting everyone. Once you've had a few conversations with Bob the Frazzled and things aren't improving, you have to watch out for your raid.
Ready Check shares all the strategies and inside information you need to take your raiding to the next level. Be sure to look up our strategy guides to Cataclysm's 5-man instances, and for more healer-centric advice, visit Raid Rx.