Most of the fighting of the Crusades is in Anatolia(Turkey) and the Kingdom of Jerusalem(Israel). Most of the people that came for the Crusades were from Europe.
The Crusades were fought by the Christians and the Muslims.
The Crusades were the battle and a battle does not fight, soldiers in the battle fight. If your question was asking what the Crusaders were fighting for and who they were fighting against see the below link.
What does the document suggest how European Christians felt about fighting in the Crusades?
The crusades were a holy war made by the christians and the Muslims who were fighting over Jerusalem
Muslims vs christians
Muslims
the crusaders were fighting muslims to capture the holy land of Jerusalem.
They were fighting over land and wealth.
feudal fighting
WHY DID PEOPLE SUPPORT THE CRUSADES?
because their religion promised that if they died fighting crusades then they would get entry into heaven