The Psalms are divided into five "books." The first two psalms, 1 and 2, serve as an introduction to the entire collection. Psalm 1 encourages us to stay on path of righteousness by meditating on the law of the Lord day and night. The psalm means this quite literally. We have fallen far from where our ancestors were when it comes to memorizing, or even being able to recall, sections of scripture for prayer and meditation. Meditation, in this context, means "chewing" on the words of scripture, being brought into a spirit of prayer by recalling them, and thinking through their meaning for your life.
Would that we would readily pick up a Bible in the morning and again at night just to pore over the words of God and implore him to help us grow in righteousness!
Psalm 2 is a victory psalm that announces the victory God gives to his son, the king. Like many psalms, it is therefore understood to be messianic, and we see its fulfillment in Jesus.
Psalm 3 introduces the concept, familiar to many of the psalms, of calling upon the Lord for deliverance from trials. This is made even more clear in Psalm 4. Psalm 5 is a lament psalm, where the writer expresses his exasperation with his current circumstances and calls upon the Lord to make things right.
Psalm 6 introduces an interesting concept in its arrangement. It consists of 5 stanzas. The first two stanzas call upon the Lord for deliverance and the last two stanzas recognize that the answer to the prayer of the first two stanzas is near. The third stanza represents the state of the psalmist -- he is at his wits end: "I am worn out from my groaning." It is at the moment of despair where we are nearest to God.