How do you read the Psalms? I think a lot of people find them hard to connect with. They are the hymnal of God’s people for millennia, but today we often don’t know what to do with them other than taking the occasional isolated phrase as inspiration for a new praise song.
I think that in regards to the Psalms, there may be real benefit in examining how Hebrew poetry works. There’s a learning curve to reading any sort of poetry; it’s language at its best, so it takes some attention.

The Psalms take you on an emotion journey. Each one starts at one point and takes you to another. The trick is following. Hebrew poetry is suggestive, preferring brevity and ambiguity, whereas our language is propositional, preferring thoroughness of description and precision. That’s why a Psalm can sometimes seem disconnected. Let’s use Psalm 142 to explain:

Psalm 142:1-2 introduce the poet’s emotion:

With my voice I cry out to the Lord;
With my voice I plead for mercy to the Lord.

I pour out my complaint before him;
I tell my trouble before him.

As you can see, each line is meant to be brief. And our English translation has made it longer than in Hebrew. There actually is no “with” at the beginning of the first two lines. The poem literally begins with
My voice, to the Lord I cry;
My voice, to the Lord I plead.
The force of the emotion is precisely in not describing it thoroughly. It’s the minimal expression of a burdened soul.

Psalm 142:3-4 describes the poet’s situation that has given rise to his complaint:

When my spirit faints within me,
You know my way.
In the path I where I walk
They have hidden a trap for me.

Look to the right and see:
There is none who takes notice of me;
No refuge remains to me;
No one cares for my soul.

While verse three begins with a statement of confidence in God, the main force of these two verses is loneliness, and almost despair.

Psalm 142:5 is a transition; it brings the poem back to the very first statement of the poem: his cry to God—and it gives us the content of this cry:

I cry to you, O Lord;
I say, “You are my refuge,
My portion in the land of the living.”

That’s it! That’s his entire cry. Of course, he goes on to pour out his troubles in the next verse, but in verse 5 he is essentially stating his right to do so: God is his refuge! God is his inheritance, so he’s going to make good use of him.

Psalm 142:6-7a are a succession of three pleas, each one followed by the reason for his plea:

Attend to my cry, (1)
For I am brought very low! (reason)
Deliver me from my persecutors, (2)
For they are too strong for me! (reason)
Bring me out of prison (3)
That I may give thanks to your name! (purpose)

This last plea is clearly more hopeful than the previous as it gives the poet’s very purpose for living, for surviving his current circumstances. “That I may give thanks to your name” causes the poet to look beyond his current circumstances and see the purpose for his entire life—and also to hold God to this purpose, calling on him to enable its fulfillment.

Psalm 142:7b is finally a full-blown statement of hope written in the same format at the previous three pleas:

The righteous will surround me, (hope)
For you will deal bountifully with me. (reason)

So the poet has brought the reader from his initial emotion of despair, through current hopeless situation, through his pleas to God, to the final statement of hope, founded on a confidence in God’s purpose for his life.

If I were to rewrite this poem with all the conjunctions and precision that we expect in English it would go something like this:

My voice cries out to the Lord,
My voice pleads to him for mercy
As I pour out my complaint before him
And tell him all about my troubles.

Even though I know that when my spirit faints within me
You are there with me,
Right now all I see is the path I’m on,
Mined with traps all over.
As far as I can see I have no refuge;
No one gives a hoot for my soul!

But yet I still cry to you, O Lord;
And here is my cry: “You are my refuge
My portion in the land of the living.”

Since you are my portion, listen to me!
Because right now I couldn’t be at a greater loss.
Come on and save me if you’re my refuge
Because they are way stronger than me!
Bring me out of prison
So I can have a reason to praise you as I was meant to!
Then the righteous will surround me,
For you will have dealt bountifully with me.

But I’m sure you will agree that this version leaves nothing to the imagination. Indeed, in my attempt to be precise and propositional, I have fundamentally altered the poem’s character. The poem no longer evokes, it explains. It is a closed poem. It is operating more on reason, and less on emotion. Whereas the original stimulates the imagination to enter into the poet’s world by its short and ambiguous but suggestive lines. It makes the reader work a little bit to do so, but also gives the emotional incentive to do so through its minimalist and accessible introduction of gut-level cries. It hooks, and then reals you in to experience its life.

Open your own Bible and give this Psalm another ride. Don’t think too much. Read very slowly, one phrase at a time, and let each phrase sink in. See what cord it strikes in you before moving on to the next. You will likely begin to have some small experience of Hebrew poetry. The more you practice it the better it will get, and you will probably find that the Psalms’ simple genius will begin to shape your own heart’s cry to God.