Pharaoh is the classic example of how God hardens hearts (Romans 9:14-18). He was given a choice when confronted by Moses to let God's people leave Egypt. Time and time again, Pharaoh refused the command of God. He saw the judgment of God through the plagues, yet he chose to refuse God's word. The word from God, which could have spared judgment on Egypt, was the word that hardened his heart.
Pharaoh was responsible for the hardening of his heart. God gave him a choice time and time again, but he continually rejected the word of God. Anyone who persistently rejects the word of God is responsible for the hardening of his own heart. Today if you will hear His voice, harden not your hearts (Hebrews 3:15).
God does not actively harden hearts. He passively hardens hearts. God gives people over to their sinful desires. A person may continually reject the warnings of God. Then, God may remove restraints to give the person over to his own disobedient desires. In other words, God gives people over to what they choose (Romans 1:24-28). Therefore, they have no one to blame but themselves.
The patience of God can harden hearts. Again, Pharaoh is an example. God was patient with him, sending the warnings over an extended time. Perhaps, Pharaoh thought the warnings were meaningless and he could defiantly refuse the word of God through Moses. God's patience was misinterpreted. That very patience of God hardened his heart.