If you are using Messenger on a Windows box, Log in, go to (on the menu bar) Tools, Options. Under the Messages tab there should be a section called Message History (at least in version 6.2).
In this section it should show you 1) if you have auto-save on, and 2) if you have it on, to where the conversations are being saved. If you don't have auto-save on, then your conversation probably wasn't saved. If it was, you can return to your Messenger contact list (close options screen), and click on File, Open Message History... From here you can click on the person with whom you were talking and find the conversation.
Maybe on other versions you might need to go to File, Open and search for your conversation in the location specified in the Options screen, but I forget.
I hope this helps