To check if you are currently signed in to Yahoo Mail, go to mail.yahoo.com
If you get a Sign-in form asking for both username (email address) and password, you are already signed out! (Make sure to do that in the same browser used to check your emails.)
If it shows a Sign-in form asking only for a password, click on "Sign in as a different user" at the bottom: this makes Yahoo "forget" your username, and you should get a blank form.
If you arrive in your Yahoo Mail inbox, you are fully logged in: click on the "Sign out" link (near top left). Click on "Mail - check email" button near the top right corner of the next screen, and you should get a blank form: if so, logout was successful!
Tip: when you logout of any Yahoo service (Yahoo Mail or otherwise), it will sign you out of all of them. That also includes properties Yahoo owns like Flickr.