1. Go to your yahoo messanger
2. select "Contacts" option on the toolbar (between 'view' and 'help')
3. on the dropdown menu select "message archive"
If you have already chosen to archive your messages, then you will already have a history of conversations. If you did not choose to archive messages when setting up your messanger, the archive feature will not be activated.
You can also enable archiving from the "message archive" link or by going to "messenger" then "privacy options" then "archive"