Welcome to BBB, Jessica. I assume you're using the latest version of WLM 8.5. Go to Tools > Options. Click on the Messages tab. In Message History (on the right) uncheck "Automatically keep a history of my conversations." If you don't choose to save your chat logs, there won't be any trace left in your computer.
WLM usually has a folder called My Chat Logs stored in your Documents folder. You can open that up, and delete the stuff that you don't want others to view.
Messenger Plus! Live has a nifty feature where you can filter off chat logging for certain contacts. If you're interested in that, post back and I'll fill you in on the details. When installing Plus! don't install the sponsor program, which is adware.