Thanks for using the Windows Live Messenger Library.
You can start a conversation using the context-menu in the contact-list control. You can monitor the user.get_conversations() collection to learn when conversations are created and start from there.
The detailed steps are given in the thread - http://social.msdn.microsoft.com/Forums/en-US/wlmessengerapidev/thread/7ae1b2de-56a4-4882-ad37-54b1db5cbc1e
It also includes a sample code.
For more details on how to use Windows Live Messenger Library with UI controls, please refer http://msdn.microsoft.com/en-us/library/dd570041.aspx
Let me know if this helps.