How do i shut down my yahoo account?

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Sorry but your question isn't specify if your mean you're want to closing your yahoo account.. first sign out your current account or if you want to deleting the same id no need to sign out and visit the Y! Account deletion link https://edit.yahoo.com/config/delete_user after opening link they should ask to your id & password to verify your account that one you want to deleting
1) Type your id & password and click on sign in tab.

Before cotinuing read there mention information, then if you wouldn't like to deleting click on "Return to Account Information"or if you satisfy proceed to cotinuing.
2) once again type password on password box and type visual code and click on "Terminate this Account" to closing your account.

Note it will take 90 days to completely delede, in during 90 days session you will able to Re-Activate by the same id & password.

if you're want to closing the same yahoo account that one you're useing on facebook and twitter,first changed your yahoo account on facebook and twitter site if you want to use in future your twitter and facebook account.