I have been doing public speaking for several years. One of the best ways to handle an impromptu conversation is to always turn the conversation to the other person. Ask about his desires, dreams and accomplishments. If you’re speaking to a group, realize that you’re there because you have a connection. Just tell them why you are passionate about the subject and you’ll always meet some of the group right on.
The number one suggestion I have is to relax and simply let it flow. Remember, that person you totally admire and wish you could be, has problems too.