If you are talking about the Yahoo Messenger that you download and install then read this:
STOP Y!M FROM LAUNCHING WHEN COMPUTER STARTS
At the top of YM click on the Messenger Menu and choose Preferences. Now click on the General category on the left. On that page, under “When I start up my computer,” uncheck the box that says “Automatically start Yahoo Messenger.” Now click OK.
TO STOP AUTO LOG-IN AND SIGN-IN OF YM
At the top of YM click the Messenger Menu. Choose Sign Out (not Sign Out and Close). Now you will see the Sign In window for Yahoo Messenger. Uncheck the boxes "Remember my ID & Password," and "Sign in automatically." Important: Now you will have to sign in with your name and password to set these changes or they will not be remembered. I also recommend go to the Messenger Menu and Preferences, General Category and uncheck the first box that would make Yahoo Messenger launch every time you turn on your computer. Click OK. Now you just click the Yahoo Messenger icon on your desktop to launch Yahoo Messenger and then type in your Yahoo ID and password. These are the settings needed for a shared computer to protect your privacy.
If you are talking about the chat feature in Yahoo Mail you can disable that. What you need to do is locate where the chat is in Yahoo! Mail and sign out of it which will make you offline on the Yahoo! Mail. On the classic mail it is located in a blue box on the left. In the New Yahoo Mail you sign out of chat by your name near the top. You will see a drop down arrow to choose from a list.
For Yahoo! Classic Mail: http://help.yahoo.com/l/us/yahoo/mail/classic/chat/mltacsignotchat.html;_ylt=AnvfSVk8GERxm1ZHr7rF.fXnAHdG
All-New Yahoo! Mail: http://help.yahoo.com/tutorials/cg/mail/cg_chat6.html
