Are you rooted? If not, open it and sign out (make sure you have no syncing or auto sign in checked). Then go to menu/settings/manage apps/FB clear data and cache. If rooted uninstall it. To totally delete it go online and delete your account.
Or...on the Accounts/Sync page in Settings you can find a tab at the bottom, after you have selected the account...Google, FaceBook, Twitter, et cetera.
It'll say "Remove account."
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