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 27: This psalm appears to contain two genres, verses 1-6 a psalm of trust and 7-14 a lament. We are not sure if they existed separately at one point and were placed together or whether they were always one psalm. There are images and themes common to both parts of the psalm and yet from verses 6-7 there is a change in tone and emphasis. There are three metaphors in verse 4 about desiring God. There are three metaphors in verse 5 about hope which refer to the Temple. In verse 13 “in the land of the living” might better be translated “in the land of life” and is a way of speaking about the Temple.
Psalm 28: a lament. Verses 1-5 are a cry for vindication. Verses 6-7 are a thanksgiving and verses 8-9 are a statement of confidence. “The Pit” is another way of talking about Sheol, the abode of the dead.
Psalm 29 : This is a psalm of praise. Commentators think this is a very early psalm and may be a Canaanite hymn that was adapted by Israel. Notice that there are also similarities between this psalm and with the Song of Moses (Exodus 15) the theophany on Mount Sinai (Exodus 19) and the enthronement psalms (46-48,93,96-99). Verses 3-9 describe a storm as a cosmic event. Notice the repetition of “The voice of the Lord”.
Psalm 30: A psalm of thanksgiving.  Notice the language, going down, death, silence and raising up, life, praise. “God” or “Lord” is mentioned 12 times, perhaps a reference to the 12 tribes. Verses 6 and 7 remind us to be humble.
Psalm 31: A lament. Verses 1-4 and 9-18 are petitions. Verses 5-8 and 19-24 are thanksgivings giving the verses in the psalm a parallel structure. Within the petitions and thanksgivings are the parts of a lament, a cry for help, statement of the psalmist’s situation, an expression of confidence in God, a prayer for vindication/expression of innocence,and recognition of God’s help. As with other psalms the last verses (23-24) move from one individual to the entire community.

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.