Maybe others could have done that as well, but Armstrong actually did it, staying calm under unimaginable pressure and averting disaster.
I used to be a really heavy traveller, carry everything I could possibly need with me, just in case. I gradually whittled that down, and now when I get nervous about forgetting something when I pack, I just tell myself that so long as I have essentials (eg wallet, passport/ticket, change of clothes, netbook), I can fix everything else. So set yourself up with small stressful situations, know that you have a relatively painless way to back out of them, and talk yourself through it.
Have faith that you can fix whatever situation you find yourself in. You may have to start out by lying to yourself in saying that, but as you try (and succeed) you'll find that yes, you can handle things. Even the ones that really worry you.
Not optimal, but definitely better than being stressed about everything.
I mean, really, what's the WORST that can happen, that's within your control?
Analyzing what happened afterwards, a few things were determined: first, given the altitude at which the malfunction occurred, my friend must have seen the problem, correctly diagnosed it, and acted in less than a second, and the total amount of time from when it offered until touchdown was something like four seconds. Second, this particular failure had occurred on this model of plane a handful of other times at such a low altitude, and had resulted in fatal crashes every other time.
So, being able to do that comes from a combination of a few things: tremendous rote training and knowledge of the plane, the ability to act calmly when your life is in peril, and an extremely efficient nervous system. Some of that can be developed, particularly the first one, and response to negative stimuli can probably be improved if you have time to think rationally, but in emergency circumstances like what an astronaut or a pilot go through, I have to say I think you're probably born that way, baby.
Neil Armstrong was a test pilot. The kind of person who is told to push designs to their limits, and is responsible for keeping things in line when it's all hitting the fan. They need to keep cool, and it can definitely be developed, as I'm sure it is for any test pilot.
It's developed through a combination of intimate (intuitive) understanding of your equipment and the situations you find yourself in, an expectation of yourself to be able to handle whatever's thrown at you, and repeated exposure to stressful situations, so that you are familiar and comfortable with them.
I don't know how much this last one applies to Neil Armstrong specifically, but many people who keep cool in the face of death can do so because they've already accepted that death is a very real possible outcome. Even when the stakes aren't so high, if you've analyzed a situation before going in to it, and have decided that you are comfortable with any likely outcome, including the worst possible outcome, then your mind is freed from worrying and can focus on executing.
Uncertainty = don't know what the f^ck is going on. Risk = these are the things that are going wrong, this is how it could get worse, this is how it could get better.
This makes it then a problem of managing information inbound/outbound, maintaining situational awareness (ie, your eyes and ears) and methodically making the best at what you've got to work with.
Very little bandwidth will be left over for "fear" or getting "nervous". On the Apollo mission, there is a story about 1202 (http://en.wikipedia.org/wiki/Jack_Garman), if you read this you will see how they handled it.
TL;DR The computer broke, and a split decision was needed to avoid a catastrophic failure.
Bales later recalled, "Quite frankly, Jack, who had these things memorized said, 'that's okay', before I could even remember which group it was in". His quick reactions and in depth knowledge led others on his team to give him the nickname "Gar-Flash".
A problem is realized. A sense of urgency develops. Assessing as fast as possible the severity, the higher the severity the less assessment needs to be done vs. moving to solving and acting.
Look for the root cause of the problem vs. effects and think of two or three routes of action, quickly. Think ~two logical steps down each route to rule out obviously bad actions. Then go with the one that is the simplest/quickest or has the best gut feeling (feeling of rightness). React.
The main thing for me, is when I get that sense of urgency, all self-concerns and distracting thoughts fall away to the process above. It is a directed panic on the inside, but to the outside observer, it looks calm and methodological. When I get to the react part, it is all I concentrate on. Panic drops for something like intense focus.
I don't know if this will help, but maybe doing similar processes for little emergencies will train your reactions for larger ones.
He states it's a fact "well known" within the military etc. that a certain percentage of folks respond very well to training for high risk, high intensity, high pressure situations (i.e facing live fire in combat) while a certain percentage simply flub and perform no better than someone who hadn't had the years of prior training.
Thing is, you don't know who's who until the event happens.
Anyway read the book it's really good in you're into this sort of idea, and into hackerish ideas in general