Suitable Topics
A good way to keep a conversation going is to talk about something you've got in common. For example if you meet someone at a party, you could ask them how they know the host or if you're standing in line for the bus, you could sigh and say "Don't you just hate waiting in line!
After that, the best thing to do is to ask your new friend about him or herself "Where lo you work? or "What do you like to do in your spare time? are good questions ten getting to know someone. Remember, everyone likes to talk about themselvest!