The way you converse is a reflection of your personality. It decides your first impression. So many things can work in your favour if you know what to say and when to say. Here are few things to remember-
The secret isn't talking in an elegant manner or anything like that. It is just the simple act of listening. The best conversationalists are the best listeners. It makes the other person feel important and pleased.
2. Take interest
Don't just sit with a blank expression, take interest in the conversation. Maintain an eye contact and nod at times. Remember you don't want to look absent-minded.
3. Don't interfere
How would you feel if someone keeps on cutting you off while talking? You would instantly lose the will to say or share anything further. Don't crack jokes or interfere while the person is talking. It's a bad habit.
4. Talk about their interests
If you ask about them they will ask about you. There are many people who just keep on talking about themselves and then they become known for self-obsession. You definitely don't want to become one of those.
Talking about their interests will also help you to learn new things. Similarly they will learn something new from you when you will talk about yours. This balances the conversation and makes it interesting.
5. Give genuine compliments
I am not telling you to flatter them, just give genuine compliments. It's not hard to find one good thing in a person. If you admire something about them, tell them. Few words of appreciation can brighten anyone's day so keep spreading smiles.
6. Ask questions
If you are running out of things to talk about and you don't want an awkward silence then ask questions about them. These questions can be like 'What is your goal in life?', 'Where were you born?', 'Do you believe in astrology?', etc. Don't ask anything personal too soon.
7. Avoid arguments
Most of the times arguments turn distasteful. Don't criticize or correct. Goal is to be a better person not the bigger person. Arguments only make people think that they are right even more than before.
I hope these points will help you in life. If you want to know more about the art of conversing then read How to Win Friends and Influence People by Dale Carnegie. He listed many instances in his book which shows innumerable benefits of being a good converationalist.