Is it permissible for a menstruating woman to supplicate during menstruation? And what is the correct way to do so?

There is no objection to a menstruating woman or a woman in postpartum bleeding reciting supplications (du'a) and reciting the Qur'an. They may also read books of tafsir (Qur'anic exegesis) without touching the Mus'haf (the physical copy of the Qur'an). As for the person in a state of janabah (major ritual impurity), it is not permissible for him to recite the Qur'an at all until he performs ghusl (ritual bath). However, he may read books of tafsir and hadith without reciting the actual verses.