1. The original sense of Psalm 16 presents some difficulties in Hebrew, and translators have always done their best to render good sense of it. It is possible that verse 4 holds the key. It might be translated, "As for the holy ones who are in the land, these even were the glorious ones. All my delight was in them."
The psalmist then speaks of his conversion to serve YHWH alone. "Those who choose another god multiply their sorrows." The psalmist will [no longer] speak their names or give them drink offerings of blood (16:4). "The LORD is my chosen portion and my cup."
2. The psalmist now looks to God for protection. "You are my lord, YHWH" (16:1-2).
What a great inheritance as an Israelite! We remember that not all of Israel worshiped YHWH exclusively, even though YHWH was distinctively the God of Israel. But what a great inheritance, to have YHWH as a heritage: "The boundary lines have fallen for me in pleasant places; I have a goodly heritage."
The LORD gives the psalmist counsel. YHWH gives counsel through the psalmist's "kidneys" (16:7), "heart" (16:9), and possibly "liver" (16:9). The LORD thus speaks to the psalmist through his inner being, his conscience, his intuitions and values.
God shows the psalmist "the path of life. In your presence there is fullness of joy" (16:11).
3. Of interest from a New Testament perspective is 16:10. The original meaning of this verse in context is straightforward. Sheol is the realm of the dead and a metonymy for death. The psalmist is saying that the LORD will protect him and keep him from dying.
The Holy Spirit led the author of Acts to hear in this verse a resonance with Jesus' resurrection. God did not "abandon" Jesus to the realm of the dead, nor let his body see corruption (Acts here is engaging the Greek translation of the psalm). The argument Peter makes in Acts 2:25-32 understands Psalm 16 in a "fuller sense," leading to the true theological point that God raised Jesus from the dead. The argument itself is based on the framework of understanding in that day.
These verses repeat what has been said more than once before. The son of the wise speaker needs to listen. Solomon will lead the son on the path of wisdom, a path that leads to long life and not stumbling.
Psalm 1 and Proverbs 1:1-7
Psalm 2 and Proverbs 1:8-14
Psalm 3 and Proverbs 1:15-19
Psalm 4 and Proverbs 1:20-27
Psalm 5 and Proverbs 1:28-33
Psalm 6 and Proverbs 2:1-5
Psalm 7 and Proverbs 2:6-15
Psalm 8 and Proverbs 2:16-22
Psalm 9 and Proverbs 3:1-4
Psalm 10 and Proverbs 3:5-12
Psalm 11 and Proverbs 3:13-18
Psalm 12 and Proverbs 3:19-26
Psalm 13 and Proverbs 3:27-31
Psalm 14 and Proverbs 3:34-35
Psalm 15 and Proverbs 4:1-9