The old covenant is completed in Christ. Jesus followed the law and told the people to listen to the teachers of the law. Jesus fulfilled the old covenant and issued in the new covenant when He died. The 10 commandments were the word of the old covenant.
We are now led by the Spirit. The Spirit convicts of sin - not the law.
Galatians is a good book to read to get the answers you are looking for.
If you follow the Spirit you have no use for the law. The Spirit will not lead you to sin.
I find this quote useful to understand how we are to live in the new covenant:
1 John 3 '8 My little children, let us not love in word or in tongue, but in deed and in truth. 19 And by this we know that we are of the truth, and shall assure our hearts before Him. 20 For if our heart condemns us, God is greater than our heart, and knows all things. 21 Beloved, if our heart does not condemn us, we have confidence toward God. 22 And whatever we ask we receive from Him, because we keep His commandments and do those things that are pleasing in His sight. 23 And this is His commandment: that we should believe on the name of His Son Jesus Christ and love one another, as He gave us commandment. 24 Now he who keeps His commandments abides in Him, and He in him. And by this we know that He abides in us, by the Spirit whom He has given us."