Romans 6:11-14
Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus. Therefore do not let sin reign in your mortal body so that you obey its lusts, and do not go on presenting the members of your body to sin as instruments of unrighteousness; but present yourselves to God as those alive from the dead, and your members as instruments of righteousness to God. For sin shall not be master over you, for you are not under law but under grace.
This whole idea of being "dead to sin" really boils down to the question: "Who is my master?" Who reigns in my mortal body? Do I allow sin to take control, or do I allow God to take control? Paul goes on, in Romans 7:21-25, to tell of two laws at war with in him. On the one hand, his inward man totally wants to follow the law of God. But he sees a different law in his flesh, the law of sin. His WILL is to follow God's law. But his FLESH, being weak, falls into temptation and does things he knows he really should be doing. He asks the question, "Who will set me free from the body of this death?" The answer is in Romans 8:1ff. The only way to be truly pronounced righteous is to walk according to the Spirit with Jesus Christ, the Son of God.
Walking in the Spirit is walking by faith in Jesus Christ. We put our confidence and trust in Him. We TRUST Him to atone for (cover) our sins. It's not that we are perfect or now walk in complete righteousness, but we let Christ reign in our mortal bodies. We obey Him. Our WILL is turned towards Him. And as long as we walk by faith, our sins are covered by His blood!
We are dead to sin, alive to God.
Nathan