This poem is an acrostic, with most pairs of verses beginning with a particular Hebrew letter. The psalm is twice as long as other acrostic psalms (like Psalm 34) because it puts two lines (roughly two verses) with each Hebrew letter.
The New Testament letter of James (see James 1: 9-12) repeats some of this imagery.
Psalm 37:3-6, Delight yourself in YHWH
We fret and worry as others manipulate and lie their way to success. This entire psalm has an anti-anxiety theme: "Relax! God is still in charge!"
Psalm 37:8-9, Hope in YHWH
Proverbial pairing: first a parallel set of statements on refraining from anxiety and then an answering parallel set of statements as to why one should do so.
This psalm is typical of Old Testament wisdom literature (such as the book of Proverbs), with short strong statements of how one should think and act, usually in doublets, parallel repetitive phrases. The New Testament letter of James develops the same "wisdom" style and echoes many of the ideas of this psalm. (Surely James knew of this song and expected his readers to recall it.)
Psalm 37:10-11, A little while...
This psalm promises success to the righteous and defeat of the wicked. Again there are two options, two choices (no more!); these are stressed in steady repetition and parallel lines.
Verse 11 is repeated by Jesus in the Beatitudes (Matthew 5: 5).
I'm glad God laughs at those who scheme and betray, since I don't seem to be able to do it!
Psalm 37:14-15, Boomerang
Note the reflective, mirror action -- the "wicked" stab themselves.
Each refrain compares the righteous and the wicked, contrasting the eventual success of the righteous with the eventual defeat and destruction of the wicked. The last chapter of the New Testament letter of James has portions which seem to parallel this psalm.
Psalm 37:21-24, On firm ground
Here is stability is emphasized; God sets the righteous on firm ground during times of storm or turmoil.
Psalm 37:25-26, Generous, with blessed children
This psalm makes some very strong claims. These last two verses (25-26) are strong simplistic statements (hyperbole?) Certainly the righteous are at times forsaken and hungry! (The New Testament letter of Hebrews, Hebrews 11:36-40 agrees with me -- we don't always see success in this life!)
Psalm 37:27-33, Inherit the land
Note the recognition that the wicked do have power and that the righteous are, from time to time, trapped. But victory by Evil is only temporary. From verse 27, the viewpoint is a longterm one (says Kidner); those who follow the LORD are assured of good things happening in a timeline that includes "forever".
Psalm 37:34-40, Man of peace
The repetitive stress of the psalm reflects the ideas at the beginning of the book in Psalm 1. "Choose the path of righteousness! Do not be misled by that apparent success of the manipulative oppressor!"
In the classical Old Testament wisdom, there are two choices and the rewards about those choices are reinforced in simple terms.