Before we begin
First off, if you have physical symptoms that you can't handle, please consider seeing a family doctor before confronting your fears. Also, don't discount this article if you don't suffer from anxiety - there are likely to be other areas in which we could use a bit of courage. Finally, if your condition is severe, or they lead to panic attacks, please consider professional help and I don't mean with the PGA pro at your course for a lesson.
Preparation
Where does fear show itself
Take over-breathing as an example. It is one of the most common symptoms. It drops the amount of carbon dioxide in your body. A quick search online will reveal that a good way to deal with this is by breathing into a paper bag (not plastic, you'll suffocate!) for a few minutes. This helps you take the carbon dioxide back in until you stabilize and calm down. It helps to be prepared in this way. Keep a paper bag in you golf bag, just don't use it when someone else is hitting it can make a very distracting sound that could cause some problems with your playing partners.
Now, there are two ways you can approach fear and anxiety. The first is to deal with it on the level of emotion. The other way is to deal with the thoughts that cause your fear. To deal with your thoughts, you need a journal, preferably one you can carry around daily, so get one.
The thoughts that cause fear
Where does anxiety come from? While it sometimes feels like pure emotion, almost all of them are based on an underlying belief or a thought. It only feels like the emotion starts first because: You didn't catch the thought fast enough or you are unaware of the underlying belief.
In Cognitive Behavioral Therapy, these thoughts and beliefs stand between you and reality. You might think an event like hitting the first tee shot or facing a difficult pitch over the bunker triggers your emotions and your reactions directly, but it doesn't. An event happens, your mind filters it through your thoughts and beliefs, and then we have the end result: Your fear, or any other reaction. Tiger Woods said in an interview that he is just as nervous as the next guy out there, it's just that he deals with his fear very differently then they do.
The problem arises when these thoughts and behaviors are unhealthy and distorted. Now, distortion is the norm for us. This is why no two people react the same way to the same event. Take that first tee shot; I for one now that when I play a lot and practice, when I get to the first tee I look down the fairway differently. I have an inner knowing a faith that I can beat the guys I'm playing or at the very least they will have a fight on their hands with me. Now when I haven't been playing nor had any practice. I can stand on the tee with completely different thoughts; stuff like don't go left and don't embarrass your self same input, different distortions, and therefore different responses. . Joe DiMaggio at age 37 was asked why he kept practicing so much; after all it was the end of his career why did he need to. He pointed up into the stands and said, "Not all of these folks have had the chance to see me play when I was younger. I don't want them leaving after a game thinking that I'm not that good." But hey what's ego got to do with it?
The key, then, is to catch your distortions if they are unhealthy. I believe healthy responses come from seeing the situation, your thoughts and beliefs as realistically as possible. (Seeing things exactly as they are is highly unlikely, and probably means enlightenment. But that's moving out of psychology, so I'll shut up now). Some people recommend positive thinking, I don't, it could be another form of distortion.
Now, the more realistically you can see your fears, the better you can split it into the logical and illogical. From there, you can take steps to deal with each.
To picture this, let's revisit my old social anxiety (first tee). It stemmed from an unrealistic view of my circumstances, which come from simply standing on the first tee. A portion of it was logical and realistic, but a portion of it wasn't. Once I knew what I was realistically afraid of, I can take steps to deal with that. The unrealistic portion would be dealt with differently.
So: How much was logical, and how much was illogical? In my case, my only logical fear was inexperience on the first tee for awhile. But there are many other possible realistic fears. What if I was out drinking the night before, instead of preparing for the day of golf? I would understandably be anxious if stepped on the tee in such a state.
What about the illogical? Briefly, they stem from three areas: Core beliefs, mental conditioning, and cognitive distortions. My core belief is that I have to play and practice to play well. My mental conditioning to believe in me as a good golfer comes from the past experience and the distortions are a part of having never stayed in the moment. The now can solve all the true nature of this distortion. When we ground our selves more in the now moment in our lives it helps us get out of our head. Thinking this thought will do you no good. Yet we can't help our self. As I had said earlier that I am not a big fan of positive thinking, it too can be a distortion. The now moment on the tee is filled with infinite possibility. What if your first bad shot that day you played the round of your life? Is that at any time a possibility? Only you can answer that.