[Reading the Psalms] is something that takes time. If you read the Psalms regularly over a long period, if you gradually internalise them, learning them by heart, and allow their words to penetrate to the deepest levels of your mind, what you begin to discover is that slowly you are ushered into another perspective altogether different from the one you know only too well, and is assumed by the world around you. What characterises this new way of 'seeing' is a constant consciousness of a transcendent Other. It is a perspective which will slowly - if you remain attentive to the words of the Psalms and the meanings found in them - reorient your mind, and lead to a different life. That is their silent transformative power.
Patrick Woodhouse, Life in the Psalms
For me, reading and praying the Psalms is something that has become inextricably wound into my practice of the Jesus Prayer. Perhaps the connection is not immediately obvious, but it has to do with this gradually more indwelling consciousness of God, Woodhouse's "transcendent Other". Thomas Merton writes that
There is therefore one fundamental religious experience which the Psalms can all teach us: the peace that comes from submission to God's will and from perfect confidence in Him.The Jesus Prayer too is a prayer, at its root, of submission to God: as a prayer for Jesus' mercy it is prayed not only in submission, our submission, but in Jesus' own submission to the Father (Luke 22.42). Our surrender is of our own will, even of our own knowing (Proverbs 20.24; Psalm 131). All that we are becomes wound into this continual prayer - not our prayer, so much as Jesus' own prayer that he offers forever before the Father (Hebrews 7.23-25). It is that which we have become caught up in, fallen indeed into "the hands of the living God" (Hebrews 10.31), with all our hearts' longings, our hopes and fears, and all whom we love.
This, then, gives us our guiding principle in praying the Psalms. No matter whether we understand a Psalm at first or not, we should take it up with this end in view: to make us of it as a prayer that will enable us to surrender ourselves to God.
Thomas Merton, Praying the Psalms
Seen like this, prayer becomes one whole, one movement of the inmost self towards God; one anticipation, almost, of our own final home in Christ: "for you have died, and your life is hidden with Christ in God." (Colossians 3.3)