How can one purify oneself according to Islam?
The Holy Qur'an explains that the basic purpose of the religion and religious guidance is purification of the human nafs. It very clearly tells that this purpose can only be obtained through practicing the religious guidance provided in the Holy Qur'an and the Sunnah of the Prophet (sws). All the religious dictates contained in these sources are well known to all including you and me. We only need to observe these directives and live the life of total submission to God. There is no short cut to the goal nor is there any parallel course of action approved by the Almighty.
The Holy Qur'an says:
هُوَ الَّذِي بَعَثَ فِي الْأُمِّيِّينَ رَسُولًا مِّنْهُمْ يَتْلُوعَلَيْهِمْ آيَاتِهِ وَيُزَكِّيهِمْ وَيُعَلِّمُهُمُ الْكِتَابَ وَالْحِكْمَةَوَإِن كَانُوا مِن قَبْلُ لَفِي ضَلَالٍ مُّبِينٍ
He it is Who has sent among the unlettered ones a messenger of their own, who recites to them His revelations and to purifies the, and [for this] he teaches them the law and the Wisdom, though heretofore they were indeed in error manifest. (62:2)
This outlines the method the Prophet (sws) adopted for the purification of the souls and the tools he used are still there with us, intact. We are only to believe in the doctrines contained in the book and practice the Shari`ah consciously having full understanding of its wisdom.
We know that the Holy Prophet (sws) would primarily read the Qur'an before those who he invited to Islam and taught it to his followers and exhorted them upon following it with spirit.