I Am New To IM, How To Retrieve The Conversation?

It depends on the IM applet you're using.
If you're using MSN Messenger, for example, you have to go to Tools -> Options and set it to save the conversations you have. Then, in the window, you can go to the File tab and click See Message History.
If you're using Yahoo messenger, you again have to set it to save logs, and those can be found, I believe, in a similar way as finding the MSN ones.
For AIM, you have to set it to save the logs as well, and can either access them by going into the conversation and clicking the "People" tab, to select Show Logs, or go into My Documents -> AIMLogger -> the folder titled with the username you want to look for the logs of -> IM Logs, and then select the logs you want.