I believe that anyone can conquer fear by doing the things he fears to do, provided he keeps doing them until he gets a record of successful experience behind him.
This is one of the most frequent topics which comes up when I am coaching. Fear of not succeeding, not getting things "right", not meeting peoples' expectations, looking foolish, not being smart/stylish/funny enough.... I'm sure you can think of a few more.
I could certainly give you a run down of things that I have been frightened of, but as Eleanor Roosevelt pointed out, if you can get a body of experience behind you, it is surprising what you can do. For example, the idea of walking into a room of people I had never met before used to fill me with absolute dread, to the extent that if I could find even the tiniest excuse to get out of it, I would. "Ooo, I'm afraid I can't come to your event - there's an R in the month". When I became a freelancer, I suddenly had no option if I wanted to meet people and get myself known. I worked at changing my mindset and instead of thinking, "they're all going to hate me!", I started to think, "hey, I will meet some really nice people tonight" or "I wonder how I can help someone tonight with a contact or piece of useful information". A change certainly didn't happen overnight, but now I really enjoy going to events where I can meet new people and hear their stories. And a couple of days ago, someone actually described me as a 'serial networker'!
I have also hated public speaking, which is one of the most common fears people have. However, through practice and receiving really useful feedback, I am getting to the stage where I am beginning to enjoy working with an audience and looking forward to developing more talks. And that is a statement I never thought I would make!
If there is something you want to do, but fear is holding you back, don't just throw the idea away and settle back in your comfort zone. You don't need to jump in with both feet - can you find a way to just dip in your toes? With networking, I started with very small meetings where I didn't feel so intimidated, or took along someone I knew so I always had a friendly face to go back to. With the public speaking, I read blogs with tips on writing and give presentations, I practiced in front of friends and got professional feedback.
Like any other project, the way to get over fear is to set yourself a target, get yourself a plan and take one small step at a time.
You might also be interested in this blog, Catch It, Check It, Change It
If this has struck a chord with you and you want to find out if coaching will support you, book for a Light the Blue Touchpaper session.