You will find an introduction to the Psalms here.

Here is a prayer to use before reading from Gregory of Nazianus (329-389), an early Church father.

Lord, as I read the psalms let me hear you singing. As I read your words, let me hear you speaking. As I reflect on each page, let me see your image. And as I seek to put your precepts into practice, let my heart be filled with joy. Amen.
Book One : Psalm 1-41
Psalm 1: This psalm is a wisdom psalm and is the introduction to the entire book. The opening phrase, “Happy are those” is also found in Proverbs. Those who follow Torah are contrasted with the wicked.
Psalm 2: This is a royal psalm, perhaps composed for a coronation. The psalmist wonders why any earthly king would revolt against God’s chosen king. “Annointed” refers to a human king and not the Messiah. This Psalm ends as Psalm one began with “Happy are…”.
Psalm 3: This psalm, ascribed to David at a particular time in his life is an individual lament.The psalm begins with the complaint (v 1-2) and then moves to an expression of trust in verses 3-6. Verse 7 is a cry for help and verse 8 is a blessing.Notice that the psalmist leaves any actions for God to perform. “Selah” is a word that appears frequently in the psalms and we are not exactly sure what it means. It may indicate a musical interlude.
Psalm 4: Another individual lament. Again there is a cry for help (v 1) a rebuke of those against the psalmist (v2-4) and thanksgiving and assurance of God’s help (v5-8).
Psalm 5: An individual lament with a cry for help and a declaration of trust. Notice how this psalm alternates, as did Psalm 1 between those who trust God and the wicked. In this psalm it seems that someone is keeping the psalmist away from the Temple and worship.
Psalm 6: An individual lament, in the church this is the first of seven Penitential Psalms (6,32,38,51,102,130,143). There is petition ( vv, 1-2, 4-5) complaint (v 2-3 and 6-7) and a statement of trust (v 9-10).  Sheminith, is  musical term of some sort.
Do you see the common features of Psalms of lament? How might these psalms inform your prayer?

Here are several good sources to aid your reading of the Psalms

Anderson, Bernhard W., Katheryn Pfister Darr, Understanding the Old Testament Abridged fourth Edition. (Upper Saddle River,New Jersey: Prentice Hall) 1998.

Clifford, Richard, “Psalms” in The New Oxford Annotated Bible with Apocrypha: New Revised Standard Version.Coogan, Michael D.; Brettler, Marc Z.; Perkins, Pheme; Newsom, Carol A. (2010-01-20) Oxford University Press. Kindle Edition.

Stuhlmueller, Carroll, “Psalms” in  HarperCollins Bible Commentary Mays, James L. ed.(San Francisco: HarperSanFrancisco) 2000.

McCann,Jr, J. Clifton “Psalms”,in The New Interpreter’s Bible Vol 3, Keck, Leander E. ed. (Nashville: Abingdon Press) 1996.