The Praise is due to Allaah Alone, and may Prayers and Peace be upon His messenger, and his family, and his companions.
So as for your statement 'When is takfeer permissible, and when is it not permissible?', then we feel that you should explain what is troubling you until we explain the ruling to you.
As for the type of takfeer in the Statement of Allaah:
"And whoever does not rule by what Allaah revealed, then these are the disbelievers.",
then it is major disbelief (kufrun akbar). Al-Qurtubee said in his tafseer : "Ibn 'Abbaas and Mujaahid said: 'Whoever does not judge by what Allaah revealed in rejection of the Qur`aan, and in denial of the statement of the Messenger (sallallaahu 'alayhi wa sallam), then he is a disbeliever.'"
As for the one who rules by other than what Allaah revealed, and he believes that he is sinning, but he rules by other than what Allaah revealed, due to bribes paid to him, or other than that, or enmity to his constituents, or closeness to them, or their friendship with him, or similar to that, then this cannot be major disbelief. Rather, it is sin, and indeed it is disbelief less than disbelief (kufrin doona kufrin), and oppression less than oppression (dhulmin doona dhulmin), and disobedience less than disobedience (fisqin doona fisqin).
And all success is with Allaah.
And may the Prayers and Peace of Allaah be upon our Prophet Muhammad, and his family, and his Companions.
 This statement is taken from al-Jaami' li Ahkaamul Qur`aan (6/188).