The first part of any conversation is an introductory phrase ("Hello, how are you doing?", "Hey, could I ask you a question?", etc). The other person will then give an appropriate response.
At this point the dialog has been started and it is then your responsibility to develop it further. This can be accomplished with something like commenting on something nearby or talking about a recent event (personal or otherwise). Give some information about it but don't ramble to the point where you are dominating the conversation. The other person will then comment on what you said and ask for more information or talk about something similar. This back and forth will then repeat as each person responds to the other person.
This exchange and change of topics is then called a conversation.
The number one way to kill a conversation is to not respond with another conversation topic. This is usually accomplished by giving one or two word statements, such as "Yeah.". This then forces the speaker to keep talking about the topic or find something else to talk about. If this repeats several times then the speaker will often stop trying to have a conversation and leave you to die. Ok, maybe not die, but they won't be encouraged to continue talking.