The Psalms are a beautiful example of the full range of human emotion at work in prayer. Many of us at some time or other have fallen under the false impression that God only wants to hear "nice" things from us in prayer. Because of this, we may only pray if we are in the "right" mood. Perhaps we think that God can't handle our anger, our depression, our frustration.
When we read these Psalms penned by a man "after God's own heart," we see that we can bring all of our burdens to God. We can approach God in whatever emotional state we may find ourselves. We won't hurt God's feelings or offend Him.
In our Orthodox tradition, we understand that prayer is something that truly takes place at the level of the heart. This is one of the important lessons taught to us by St. Gregory Palamas, whose memory we celebrate every second Sunday of Lent. In Romans, Paul writes that "He who searches the hearts knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God." (Romans 8:27) In this context, Paul is using the word "saints" to refer to all Christians. God knows our hearts even better than we ourselves do! We have simply to come to stand in the presence of God, dropping all pretense and falsehood (including our self-delusions!), and the Spirit will intercede for us.