The first use to discuss is the civil use. The civil use of the law is primarily focused upon how the law restrains evil in sinners within society. It is this use of the law that the apostle Paul discusses in 1 Timothy 1:8-11 when he says that the law is laid down for the "lawless and disobedient." This function of the law is to establish order and regulation in society so that people will not act simply as they see fit, but actually have consequences for their actions. In regards to the sixth commandment, this use of the law establishes a paradigm for structure in society. Murdering is unacceptable and should not be tolerated among any societies. Furthermore, this is the case not because of some general consensus or majority vote, but due to divine fiat. The creator of all things has declared that man shall not murder one another. This command establishes a basis for government's to "bear the sword" or punish those who would violate their creator's command. While capital punishment for such a crime is not proven per se, punishment of some type is hinted at and expected if such a law is to be enforced consistently.
The second use of the law is as a mirror. In particular this use of the law focuses on convincing us individually of our sin. Paul hints at this use when he describes the law as our "schoolmaster" in the book of Galatians. Here the law is read by an individual and they begin to realize that something they have done is wrong by the standards of God. This use is associated closely with the convicting work of the Holy Spirit. Using the law as a mirror, God makes us to see ourselves in our true light: as sinners. In regards to the sixth commandment, this use convicts people who have murdered of their sin, ideally with the end of bringing them to Christ as their only hope before their God. In the sermon on the mount Jesus makes this use even more powerful, as he proclaims that everyone who hates is brother is a murderer as well. Jesus gets to the heart of the matter showing that even committing the act is unnecessary, it is the thoughts and intentions of our hearts that make us filthy sinners before a Holy God.
The third use of the law is as a guide. This use of the law is especially relevant to believers. The law as a guide establishes the parameters of how God would like his people to live. In a sense this is God's revealed will to us, and we are expected to conduct ourselves in such a way that he would be pleased. For the sixth commandment, this makes it clear that God does not want his people to be characterized by murder. Far from having the prerogative to live however they like because they are "under grace;" God's people are expected to know his desires for their conduct and live accordingly. Murder itself can be a sticky subject in terms of how it is to be defined. It seems that manslaughter, killing in war, and murder are differentiated in the OT itself. However after careful study of God's Word, whatever murder is defined as, God's people should not be engaged is such practices.
The commandments and laws of the OT are just as relevant for God's people today as they were during the time of Moses. The question is not whether they are relevant, but rather how they are relevant. A careful consideration of the three uses of the law can keep us on track and stop us from heading too far into the directions of legalism or licentiousness.