In order to be a great conversationalist, be an active listener. Ask them questions and encourage them to talk about themselves and their accomplishments. At the end of the day, people are more interested in talking about themselves or their own interests than yours.
Here are three questions that can help you get to know someone better.
1) For what in your life do you feel most grateful?
If you are grateful for something in your life you are appreciative. Whether it is a person, place, or experience, the thing you are most grateful for at some point made or continues to make an impact on your life. Being grateful for something also helps you understand what you value most in life. Is it fame and fortune you are seeking? Or do you value the simple life?
2) If you could change anything about the way you are, what would it be?
Accepting who you are is a big part of becoming a more resilient person. With societal pressures looming in every corner, being comfortable in your own skin can sometimes be a challenge. Ultimately we are who we are because of our experiences including how we were raised. One reason why you would want to change the prior experiences is because it is still affecting your present or will have an effect your future. Just understand that there is always a trade-off. You can't be a party-animal free spirit and also be a quantum physicist.
3) What does friendship mean to you?
Adding a friend on Facebook is as easy as clicking a button. We so often casually refer to people we know as friends even if we've only met that person once! However there are differing degrees of friendship. Those that you recognize and will say hi to on the street, but wouldn't reach out to on a daily or weekly basis. Then there are others who you spend more time with and see more often. When they've hit a rough patch in their life, you are there to comfort them and console them. Who are your closest friends?