One major interpretive question in the Psalms is how to understand its high view of the law in a Christian context. Take, for instance, Psalm 19:7-9:
The law of the LORD is perfect, converting the soul; the testimony of the LORD is sure, making wise the simple.
The statutes of the LORD are right, rejoicing the heart; the commandment of the LORD is pure, enlightening the eyes.
The fear of the LORD is clean, enduring for ever; the judgments of the LORD are true and righteous altogether.
The feeling toward the law expressed her is so foreign to me that I don't know how I ought to respond to it, or how it is relevant to a time in which the law has been fulfilled in Christ.
Calvin makes some helpful remarks on this point which are worth quoting at length:
But here a question of no small magnitude arises; for Paul seems entirely to overthrow these commendations of the law which David here recites. How can these things agree together: that the law restores the souls of men, while yet it is a dead and deadly letter? That it rejoices men's hearts, and yet, by bringing in the spirit of bondage, strikes them with terror? That it enlightens the eyes, and yet, by casting a veil before our minds, excludes the light which ought to penetrate within? But, in the first place, we must remember... that David does not speak simpy of the precepts of the Moral Law, but comprehends the whole covenant by which God had adopted the descendants of Abraham to be his peculiar people; and, therefore, to the Moral Law - the rule of living well - he joins the free promises of salvation, or rather Christ himself, in whom and upon whom this adoption was founded. But Paul, who had to deal with persons who perverted and abused the law, and separated it from the grace and the Spirit of Christ, refers to the ministry of Moses viewed merely by itself, and according the the letter. It is certain, that if the Spirit of God does not quicken the law, the law is not only unprofitable, but also deadly to its disciples... The design of Paul is to show what the law can do for us, taken by itself... but David, in praising it as he here does, speaks of the whole doctrine of the law, which includes also the gospel, and, therefore, under the law he comprehends Christ.
I don't think I'm willing to follow Calvin all the way here and say that the gospel is included in the law in the Psalmist's usage, but I think the observation that Paul was dealing with a perverted understanding of the law is crucial. I should mention, by the way, that I am not going to consider any interpretations which claim that these verses are simply not relevant to the Christian because the law has been done away with. I have a higher view of the law (and the Psalms) than that.
This is what I think may be going on: A full understanding of the law, which the early Jews possesed, understands that it is not possible to obey the law simply by trying to do it. That Judaism was a life and not a strict adherence to a set of moral and ceremonial laws is made explicit many places: Rend your hearts and not your garments. The sacrifices of God are a broken spirit. Psalm 19:9 even seems to equate the fear of the Lord with the law itself, which I take to be more confirmation that the doing of the law was intimately connected to and founded upon a person's holiness.
In fact the very existence of Hebrew wisdom literature testifies to this. Why did the Hebrews develop wisdom literature? Wouldn't you have expected reams of legal literature instead?
Not if they understood that the only way to please the Lord was to be formed into the sort of person whose obedience flows from his righteousness, and not the other way around.
This is why I can proclaim with David "the statutes of the Lord are right, rejoicing the heart". In doing so I am not swearing fealty to a set of laws as the path to salvation. The law has never been that, and Judaism ay its best recognizes this. In extolling the law alongside the Psalmist, I am declaring both the beauty and perfection of God's unchanging moral decrees and the importance of the character transformation which will allow me to follow them. But unlike David, I can look beyond the law and see in those words He who pefectly fulfilled it. Jesus is a more accurate picture of the moral character of God, and so much more than that. The New Testament infuses the phrase "the statutes of the Lord are right, rejoicing the heart" with meaning far beyond anything dreamed of by David. As the author of Hebrews tells us, "all these [holy men of old], having gained approval through their faith, did not receive what was promised, because God had provided something better for us, so that apart from us they would not be made perfect."
 Of course, they did produce this legal literature later. But it was not their immediate response to the law.