1. Fear of talking to strangers. As children most of us were admonished to "never talk to strangers" the inference being that strangers are dangerous and not to be trusted.  But in most networking settings the strangers are just like you, often work in the same field and may even share some of your hobbies and values. To overcome your fear try tricking your brain into seeing the strangers as long lost friends or distant cousins you're meeting for the first time at a family reunion.

2. Fear of rejection.  This is the root of our biggest fear of networking.  Many of us are simply afraid that people won't be receptive or responsive to our attempts to network.  To overcome this fear, create limits with yourself.  For example, you may decide that you will say "Hi, is this your first time here?" to someone and if they are not very talkative or receptive give yourself permission to move on.  

3. Fear of being boring or having nothing to say.  Well the good thing about networking and having conversation is that often the best conversationalists are those who listen.  Focus on listening to the other person when networking and ask questions directly related to what they are talking about, (i.e. their career, job, aspirations, recent project, award etc.).  You will soon discover that people enjoy talking about themselves and are highly appreciative of those who are good listeners.