The Parable of the Prodigal Son, which some of us had this past Sunday, teaches and demonstrates the difference between vain works of the law and the good works of faith. Consider the wayward younger son, sitting in a pig farm, coming to himself. He says, "Father, I have sinned against heaven and before you. I am no longer worthy to be called you son. Treat me as one of your hired hands." This son has a specific idea of what works ought to be - they are the things that we do in order to get back in good with God (or with dad, as the parable goes), to make up for our own errors, to atone for ourselves.
Of course, in the parable, the father has none of this. When the father welcomes back the son, all he can say is the first two lines - "Father, I have sinned against heaven and before you. I am no longer worthy to be called you son." Nothing more than that is said - the father cuts him off before he can make misguided promises of work and the like. Rather, the father shows love and declares this miserable man to be his son, dresses him in robes and puts a ring on his finger. He is not a servant, he is a son - and not only is he going to look like a son in his robes, but he will have the authority that a son has -- see, he has a ring.
The younger son will work, will do stuff - but he will not be as a hired hand, he will not be a mercenary trying to make things up to his father. He will work as a son, work out of love and joy that his father still calls him his child.
Likewise, as a Christian, our works have nothing to do with making God like or accept us - they have no benefit to our standing with God. Rather, they flow and follow from the relationship He has declared us to be in with Him through the forgiveness won by Christ Jesus. He has called us His children, and so we are - and we do the things proper to children, we learn more and more to behave like our Father, to do Fatherly things - because that is who He has made us to be.
The sinful human thinks works are needed to make our relationship with God different. A Christian knows that works happen because God has made our relationship to Him different. The two are as different as can be.