Historically, Christians have utilized the Psalms as the language describing their communion with God. In a sense, they have understood them as the poetry of the believer's soul in response to the redemptive work of God. As such, persons often find themselves praying and singing the Psalms in the first person as a means for expressing themselves to God, so that the words of the Psalmist become the words of the worshiper.
Let me go on record in saying that this is a good thing, I highly recommend it, and I do it myself. Yet, when we read the Psalms this way, we must be careful not to fall into the error of reading them first and foremost "me-centrically" or "egocentrically," for they are not primarily about "me."
The Psalms are first and foremost about Christ. As Geerhardus Vos has aptly stated, "The content of the Psalter is eschatological and messianic." Every Psalm either expresses the words of Christ or words about Christ. To read the Psalms correctly, then, we must first read them to hear Christ and to see Christ. But reading the Psalms "Christocentrically" does not mean that you cannot also read them as your own words; rather, reading the Psalms Christocentrically is the means by which the words of the Psalms become your words. In fact, I would assert that reading the Psalms Christocentrically necessitates that the words become your words.
The gospel itself teaches us that when the Spirit gives us faith, he uses that faith to unite us to Christ. The answer to question 30 of the WSC states, "The Spirit applieth to us the redemption purchased by Christ, by working faith in us, and thereby uniting us to Christ in our effectual calling," (emphasis mine). The apostle Paul teaches us that this union with Christ means that we have been "crucified with Christ. It is no longer [we] who live, but Christ who lives in [us]. And the life [we] now live in the flesh [we] live by faith in the Son of God, (Gal 2.20).
Because of faith and our union with Christ, his life becomes our life--his story becomes our story. When we read the Psalms Christocentrically to hear Christ's words about himself and to see the truth about Christ--we find Christ and ourselves. And it is only when we first find Christ and then ourselves united to him that the words become our words. We must do the work to first hear and see Christ, before we look for ourselves. The Psalms are your Psalms in Christ; outside of him, the Psalms have no meaning for you. So do read and sing the Psalms as the language of your communion with God, but do so as those united to Christ and as those who have entered into his communion with the Godhead.
Having put forward my understanding of the Psalms, here is a recent sermon on Psalm 24. You can listen to it here. (Audio cut off the end)