SOnTheM 14

"You have heard that it was said to the people long ago, 'Do not murder, and anyone who murders will be subject to judgment.' But I tell you that anyone who is angry with his brother will be subject to judgment. Again, anyone who says to his brother, 'Raca,' is answerable to the Sanhedrin. But anyone who says, 'You fool!' will be in danger of the fire of hell." Matthew 5:21-22

The phrase "you have heard that it was said" refers to the things which the people had been taught their whole lives. When Jesus says "but I tell you," He isn't saying that they were taught wrong, that is to say, that the Old Testament Law was wrong and He is right, but rather that the people took the Law far too literally and did not apply the principles from it to other areas of their lives. Jesus already stated that He was not there to abolish the Law, but to fulfill it (Matthew 5:17), so why would He contradict the Law? He wouldn't. He was simply giving a new interpretation of the Law, which is, of course, the correct interpretation.
Just like in our society, a murderer would be tried and face the judgment of the court. Jesus states that anyone who is angry is also subject to judgment, but how can a jury decide whether a person is guilty of being angry? This fact points to the idea that the judgment is the judgment of God, not of men. The important fact is that "the root of murder is anger, and anger is murderous in principle" (Expositor's Commentary). Refraining from murdering someone may keep you out of prison, but harboring anger and bitterness towards someone is known by God, and His judgment awaits that person.
Remember that your heart is what God is concerned with, and your actions will follow your heart.