Start a conversation by asking questions about the other person. Try not to talk about yourself too much—if they want to know (or are polite) they'll ask. Be confident and charming. Do not hog the conversation, that is arrogant and boorish. Look interested and listen to the answers.
Don't look over the person's shoulder or around the room when they are talking, or let your eyes linger on the hot new guest who just walked in. That implies you are distracted or not interested—that your conversational companion is too trivial or tedious to bother paying attention to.