Types of Psalms
Because the psalms were originally written as a response to Israel's religious, political and cultural history, they deal first and foremost with how people react in the ordinary circumstances of daily life. So among the different groups of psalms we find:
Royal psalms (2,18,21,72,110,132,144 etc) were written for enthronements of the kings, prayer before battle in time of war, thanksgiving after victory etc. Christians spiritualised these to take on the meaning of God's kingship and the messiahship of Jesus.
Hymn psalms (8,19,29,33,46,48,65,67,68, etc) usually invite us to praise God, then tell us why we ought to do this before concluding with a blessing or a request.
Thanksgiving psalms (30,32,40,66,124 etc), as their name implies, tell how God has rescued a person or given them a particular gift and then they bless God for the saving action.
Historical psalms (78,105,etc) trace how God has had a hand in the history of the nation and exhort us to remain faithful to our covenant with God.
Confidence psalms (23,27,121 etc) are prayers or songs that inspire us to trust in God, often in the face of adversity.
Lamentation psalms (3,5,13,22,26,44,60,74, etc), either individual or group, ask for God's help in a particular need, explaining why the Lord should act and expressing confidence in God's swift aid.
There are also other mixed categories, including prophetic psalms and wisdom psalms that reflect on various problems and then try to offer a solution.