Here is my understanding of "the law":
From the beginning of time, there was one principle that God used to create the heavens and the earth--that principle was love. Out of this love, God saw that His people needed not only a standard for their lives but also SOME WAY of interacting with Him (because of the fall). So, he confirmed what some folks call "the Noachide laws", confirming it by the rainbow in the sky. Let folks speculate whether or not it applied to Gentiles--their foolish speculation doesn't damage what God's Word says. Also bear in mind that civilization at the time was quite primitive and that all they had for a standard was oral tradition and the "status quo's" conscience. All this time though, God promised Abraham that He was going to
When Moses came along, God decided to establish another standard, adding the "Noachide Laws" to it (http://en.wikipedia.org/wiki/Noachide_Laws). Then...this is where Pastor David Wilkerson's Book "The New Covenant Unveiled" kicks in which he discusses in-depth how that Israel was not able to keep the Old Covenant, mentioning also that God had...swung a deal with His Son that HE would come to earth, fulfill the prophecies CONCERNING the FIRST COMING of Messiah, simultaneously paying off our debt of sin by taking the responsibility of our debt upon himself.
Mind you, not EVERY prophecy concerning the Messiah has come to pass yet--BUT the prophecies concerning His FIRST COMING and of our REDEMPTION FROM SIN has! So, now, through Christ, we are "in the boat"--we are "in Christ". BUT...we must AVOID those rocks that would shipwreck our faith--as Paul spoke of, using the analogy of a wreck as a picture of apostazing, turning your back on God and going the other way. PRAISE GOD! We are IN!
So...what's it mean to live in the New Covenant?
Well...it means that...
1. The law is good and should be followed--BUT NOT TO BE JUSTIFIED!
2. Follow the "Royal Law"; love the Lord your God with all your being and everyone else as much as yourself. Following this lifestyle results in a person's life "complimenting" the law (as Paul says, "Yea, we establish the law.")
If you will also go to Wikipedia and read the article entitled Legalism, you will discover something that used to trouble me quite frequently in my understanding of the New Covenant. See, in Greek, there exists no such word as "legalistic, legalism"; BUT rather, truth be told that in the original Greek, when Paul talks about the law in a negative light, he is saying and implying that one should not follow the law in order to be justified (which is basically...legalism). The deal is, I think that while the translators meant well, they didn't do a very good job of translating those parts of the text concerning the law.
Lol; at Bible school, I would also wrack my brain and storm the concordance, looking for that word "legalism, but would never find it.

So I hope this all makes some kind of sense.
