Whether it's at the beginning of class, spur of the moment, or simply to kill some time at the end of class, these conversation tips will help you (teacher or student) carry on the conversation.
1) Be interested. This should go without saying and sometimes it's difficult to remain interested, especially at the end of class. Asking questions simply for the sake of asking or, worse yet, waiting until it's your turn to speak. Be sure to make eye contact but don't stare.
2) Find common ground. One of the benefits of being a foreign English teacher is that your host country becomes a place to explore. Not only does living there begin to challenge what you read and understood before you got there, but it becomes a constant learning process. Food, music, culture, religion, people, language, it's all up for debate and discussion as you settle in. Your students will love the fact that you're taking the time to learn about their home and country and, in exchange, you'll love learning about it from their perspective.
3) Don't be afraid to challenge what's been said. It's okay not to agree with everything that is said. As a matter of fact, discrepancies can often lead to some of the most interesting conversation topics.
4) Don't tease... much. Know and understand the difference between playful and offensive teasing. In general, politics, sex and religion are sensitive subjects, but so are looks, manner of speech, dress and personal preferences or, even more important, mistakes or previous errors. As a teacher, it's your job to ensure a safe environment in which students can practice their English without fear of ridicule or censure. What goes on outside of the classroom isn't much of your business, but inside, it's your job to facilitate conversation and discussion. Let different views be heard and moderate the discussion so everyone has a chance to speak.
5) Smile. There's nothing that helps a conversation along better than a pleasant smile or an appropriate laugh.
6) It's okay to use hand gestures. Some people are more animated than others, but it's okay to use your hands to emphasize a point or draw a diagram in the air, etc. That doesn't mean you have to wave your hands frantically in the air
7) Learn how to read people's body language. This is especially important if you're talking about sensitive subjects. If people aren't interested in talking it's going to be a long day for both you and them to try to keep the conversation going. You can minimize this by finding common topics or getting them to talk about them.
8) Find a common topic or theme. Make a note of any topics or themes that keep popping up in discussion or in the textbook. If it keeps coming up, talk about it.
9) Talk about them, not you. People love talking about themselves. Master this and people will love you.
10) Know when to move on to the next subject. Sometimes a subject just dries up or no one wants to talk about it. If you can't encourage your students to talk any more, try an anecdote or a short story. If that fails, move on. There's no point wasting time on something that isn't going to happen.
I hope that helps!