If you would like to sign out of one Yahoo! Mail account and in to another, simply do the following:

1. Click "Sign Out" just below "Welcome, yourname" at the top of the page.
2. Next, click the "Return to Yahoo! Mail" link.

Your browser returns you to the Yahoo! Mail sign-in, where you can enter a new Yahoo! ID and password.

Additional Information: It's possible to use the same computer for multiple Yahoo! Mail accounts. However, it isn't possible to be signed in to two accounts at the same time. Opening a new browser window and signing in to one Yahoo! Mail account automatically signs you out of any others.
(The only exception to this is if you have access to two different browsers on the same computer—for instance, Firefox and Internet Explorer. In this case, you could use each browser to sign in to a different account. Because browsers have separate cookie files, they allow you to access the two separate accounts without having them interfere with each other.)