Sign into Yahoo Mail; click on your name (top left corner) and select "Account Info".
Yahoo will ask for your current password for your protection: this is normal, so type it in.
Scroll down to "Sign-in and Security" in the new window and click "Change your password".
Type in your current password in the next screen (this prevents others from changing it if you leave Yahoo Mail unattended), and type twice the new, case-sensitive password you want.
Click on the "Save" button, and Yahoo will apply the change immediately.
This affects all Yahoo properties and/or other websites that use Yahoo profiles for authentication: Yahoo news, Flickr, etc. Also, if you check your Yahoo emails from an email program, remember to update your password in there as well. If your web browser "remembers" your Yahoo credentials, you'll need to re-enter them the first time to avoid sign in errors.