Great conversationalists are actually good listeners. Obviously, you need to draw the other person out by asking interested questions on all kinds of subjects. When your date answers, listen attentively to the answers and ask more pertinent questions. There is more. Research shows that humans are drawn to and fall in love with people who like them.
So, tell the person that you are interested in lots of positive thinks about himself. What is pleasing about him; what you like about his personality, etc. . When someone has a good feeling when he is with you, he will want to repeat the experience and have another date. One date leads to another, and during this time you are forming a relationship. You also need to know that even if you put the above techniques into play, your lack of confidence may still play tricks on you. Even if you don't say a word, a man can read that you feel terrible about yourself, and this is a turn off. For this reason, you would be wise to do some therapy and find out where your lack of confidence stems from.
I am sure that your insecurity isn't only the result of a social skills deficit. I would bet that someone made you feel pretty low when you were a kid. When you figure out where your lack of confidence stems from and work to resolve the problem at its source, you will begin to feel better about yourself and more attractive. When you feel better, you will find that relating comes easier, and the above techniques that I suggest will come to you naturally. Let me know how you make out.