No Priests

No Priests, then who guides the Muslims in their prayer?

The person who leads the prayer is called Imam in Arabic.

A person who has good knowledge of Islam and is able to recite The Qur'an well and lecture to the gathering during the Friday noon prayer is appointed as the Imam of a mosque.

Is the Imam an intermediary between God and man?

The Imam is not like a priest. He is not an intermediary between God and man. Muslims seek the Mercy of God directly.