Nowadays there are many groups in Islam led by Ulama (scholars). Some of these groups hold conflicting opinions although they cite Qur'an and Hadith for their views. They even accuse each other of being astray. How can we know which of these groups are correct?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Whoever sticks to the way of Salaf Saleh (good predecessors) as far as the Aqida (faith) and other Islamic issues are concerned and who follows only what is in conformity with the Qur'an and the Sunnah, he is on the right path of Allah. But whoever does not completely stick to this, one can take of his sayings what conforms to Sharia and leave what does not.
The Salfi way is that which is based on following the way of the pious believers from Salaf Saleh (righteous predecessors) and those who followed them in applying righteous deeds till The Last Day. They are the ones described by the Prophet in the following Hadith: "A group of people from my Ummah will always remain triumphant on the right path and continue to be triumphant (against their opponents). He who deserts them shall not be able to do them any harm. They will remain in this position until Allah's Command is executed (i.e. Qayamah is established)." [Reported by Imam Muslim]
So whoever adheres to this way (Salaf Saleh), he should not be a member of any of the following groups: the Khawarij who kill Muslims for committing sins nor a Rawafidh: who says that some of the companions of the Prophet are unbelievers, nor he a "Muawwil"(interpreter) who uses falsehood to deny the Attributes of Allah or some of their meaning, nor a pantheist who regards God as identical with the material universe, nor a Sufi who worships graves and offers them vows.
The Salafi is one who follows the way of the companions and the Good Khalifs. As for the other ways, they have made right judgements about some issues and made wrong judgements about others. These ways differ from one another according to how close they are to Salaf way.
Allah knows best.