The usual route is to travel to Nasiriyah and then continue to the Chibayish area, where boats depart from near the Martyrs Mosque. From Nasiriyah, shared or private taxis can reach the boat area.
Exploration is done by traditional boats (mashoof or balam) with local guides from the Marsh Arab communities. It is best to arrange a guide or tour in advance. For more info: Iraqi Marshlands (Ahwar)