How does one repent from disbelief (kufr) and polytheism (shirk), and is it permissible to declare people of innovation (ahl al-bid'ah) disbelievers?

The repentance of a disbeliever (kafir) or polytheist (mushrik) is by declaring the Shahada: "There is no god but Allah, and Muhammad is His Messenger," and affirming what it entails. As for declaring an innovator (mubtadi') a disbeliever, this is a grave matter that requires two conditions: First, verifying from the Qur'an and Sunnah that the act in question is indeed disbelief (kufr). Second, verifying that this description applies to the individual, such that proof has been established against him, he understood it, yet refused and showed arrogance. A statement or action might be disbelief, yet the one who says or does it is not a disbeliever, such as one who is coerced or mistaken. Therefore, it is necessary to be certain and deliberate before uttering the word "disbelief."