Hi Derik,
There's some sound advice for you above.
I know that what follows may not seem to be the help you requested. But since you ask, "Where would you begin?" I have a comment or two on the heart of the Psalm's author.
The author is thought to be King David, and in my opinion, it sounds a lot like things I know about David's life. David, a man after God's own heart, (1 Samuel 13:14; Acts 13:22) was a true saint —and a sinner. Think of what it means to be a man after God's own heart as we look at Psalm 119 and several other Psalms of David.
In the first three verses, David pronounces a blessing on a group of the Godly he refers to as "they." David doesn't know these people for they are an idealized fiction. They don't exist. (Ecclesiastes 7:20)
Psalm 119:1-3
1 Blessed are they that are perfect in the way,
Who walk in the law of Jehovah.
2 Blessed are they that keep his testimonies, That seek him with the whole heart.
3 Yea, they do no unrighteousness;
They walk in his ways.
Then David's thoughts turn from fiction to reality as he considers his own fallen heart.
Psalm 119:5-6
5 Oh that my ways were established
To observe thy statutes!
6 Then shall I not be put to shame,
When I have respect unto all thy commandments.
David often lamented his transgressions against the Lord. His was indeed a life of faith and repentance. Here are a few examples:
Psalms 39:8
Deliver me from all my transgressions: make me not the reproach of the foolish.
Psalms 51:1,3
1 Have mercy upon me, O God, according to thy lovingkindness: according unto the multitude of thy tender mercies blot out my transgressions.
2 For I acknowledge my transgressions: and my sin is ever before me.
Psalm 38:1-6 (see the whole Psalm)
1 O Lord, rebuke me not in your anger, nor discipline me in your wrath!
2 For your arrows have sunk into me, and your hand has come down on me.
3 There is no soundness in my flesh because of your indignation; there is no health in my bones because of my sin.
4 For my iniquities have gone over my head; like a heavy burden, they are too heavy for me.
5 My wounds stink and fester because of my foolishness,
6 I am utterly bowed down and prostrate; all the day I go about mourning.
So Derik, where would you begin to learn the Law of God?
Begin by agreeing with God that in you (that is, in the flesh) dwelleth no good thing. (Romans 7:18) Then make much of the love and grace of God
"Who hath delivered [you] from the power of darkness, and hath translated [you] into the kingdom of his dear Son." (Colossians 1:13) Accept the fact that by nature, your heart is
"deceitful above all things, and desperately wicked." (Jeremiah 17:9) Then come to God in prayer seeking the help of the Holy Spirit to guide you into all truth. Pray through these and like considerations until your heart and mind is adequately affected by such thoughts. Humbly pray,
"Open thou mine eyes, that I may behold wondrous things out of thy law." (Psalm 119:18) Then hear God's answer to you in Scripture,
"I am the Lord thy God, which brought thee out of the land of Egypt: open thy mouth wide, and I will fill it." (Psalms 81:10) Now you are ready to learn the Law of the Lord.