This is a wonderful way to pray. Every human emotion is expressed in the psalms, so it is not difficult to find a psalm to suit our mood. It is the way Jesus Himself prayed, and, the fact that they were dear to Him is borne out by the fact that He often quotes from the Psalms (Mathew 21:16 & Luke 4:10 for example). Even as He was dying, He was praying the psalms. They are particularly useful when we cannot find the words to pray, because we are sure to find something which suits our needs.
For example, Psalm 138(139), which starts off by saying:
"O Lord, you search me and you know me,
You know my resting and my rising."
Becoming aware of this, we are brought into the presence of the Lord, who is always with us. We become conscious that He is intimately aware of everything about us, and knows us better then we even know ourselves. To pray with the psalms, you can use either of the above methods, to which they are ideally suited.
"Psalms to suit different moods" for the references of Psalms.