The Law was added because of transgressions, as Paul says in Galatians 3. Its entire purpose was to "make" sin appear as dreadful as it really is:
The very commandment that promised life proved to be death to me. For sin, seizing an opportunity through the commandment, deceived me and through it killed me. So the law is holy, and the commandment is holy and righteous and good. Did that which is good, then, bring death to me? By no means! It was sin, producing death in me through what is good, in order that sin might be shown to be sin, and through the commandment might become sinful beyond measure. For we know that the law is spiritual, but I am of the flesh, sold under sin. - Romans 7:10-14
The commandments within the Law are, themselves, Holy, and Righteous, and Good because of the nature of the God from which they proceed but they cannot produce righteousness, holiness, or goodness in humanity because of the nature of they to whom the Law is given since, as Scripture says, "There is no one righteous; no, not one.":
Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God.
For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. - Romans 3:19-20
Setting about to establish one's own righteousness by keeping the Law is a trap since the only thing that can be acquired that way is knowledge of sin:
But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins. It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus. Then what becomes of our boasting? It is excluded. By what kind of law? By a law of works? No, but by the law of faith. For we hold that one is justified by faith apart from works of the law. - Romans 3:21-28
This knowledge of sin, then, should lead or drive us to repentance and faith in Christ:
Is the law then contrary to the promises of God? Certainly not! For if a law had been given that could give life, then righteousness would indeed be by the law. But the Scripture imprisoned everything under sin, so that the promise by faith in Jesus Christ might be given to those who believe. Now before faith came, we were held captive under the law, imprisoned until the coming faith would be revealed. So then, the law was our guardian until Christ came, in order that we might be justified by faith. But now that faith has come, we are no longer under a guardian, for in Christ Jesus you are all sons of God, through faith. - Galatians 3:21-26
Once faith comes, one's nature is changed by the indwelling Holy Spirit working to conform us into the image of Christ:
Likewise the Spirit helps us in our weakness. For we do not know what to pray for as we ought, but the Spirit himself intercedes for us with groanings too deep for words.
And he who searches hearts knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God. And we know that for those who love God all things work together for good, for those who are called according to his purpose. For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers - Romans 8:26-29
Only God is righteous and the Law given by God represents that single righteousness which is required of us and which we can never become or attain. The eternal Son was "commissioned" by the eternal Father to so identify with us as to become what we are so that we may become what He is:
Therefore, if anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come. All this is from God, who through Christ reconciled us to himself and gave us the ministry of reconciliation; that is, in Christ God was reconciling the world to himself, not counting their trespasses against them, and entrusting to us the message of reconciliation. Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God. For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God - 2 Corinthians 5:17-21
Only in Christ is it possible for the righteousness revealed and required by and in the Law to be fulfilled (and take careful note of the verse below), not by us but in us:
There is therefore now no condemnation for those who are in Christ Jesus. For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death. For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit. - Romans 8:1-4
The process of this sanctifying work of the Holy Spirit, once begun, will never stop because of God's faithfulness:
And I am sure of this, that he who began a good work in you will bring it to completion at the day of Jesus Christ. - Philippians 1:6
How does one enter into this process? Give up! Repent of being an unrighteous sinner trying to ignore God's righteousness or to establish one's own by whatever means and cry out for God to save you in Christ. He will do what He has promised provided you receive the Christ that is LORD:
For Moses writes about the righteousness that is based on the law, that the person who does the commandments shall live by them. But the righteousness based on faith says, “Do not say in your heart, ‘Who will ascend into heaven?’” (that is, to bring Christ down) “or ‘Who will descend into the abyss?’” (that is, to bring Christ up from the dead). But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith that we proclaim); because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. For the Scripture says, “Everyone who believes in him will not be put to shame.” For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him.
For “everyone who calls on the name of the Lord will be saved.” - Romans 10:5-13