Here is something from Ignacio Larranaga, OFMCap on the brief guidelines on how to pray the Psalms:
Spend a few moments of silence. Let your soul be empty, open, tranquil, unperturbed, and calmly expectant, because it is the Lord who is coming, in His Word, to have an encounter with you.
Begin by not looking for any particular purpose, such as a solution to your problems, doctrine, or other truths. The Lord will manifest Himself freely, in accordance with His designs and plans for your life.
Pray the psalms slowly. Do not read. With a journal handy, write down the Psalms that say something to you. Identify different feelings you encounter within yourself, such as those of admiration, thankfulness, understanding, etc.
Make an effort to feel the meaning of each phrase with all your soul. Identify your attention and emotion with the content of the expressions, and express them with the same inner feelings that the psalmist had.
In the spirit of the Psalms, imagine yourself within the Heart of Jesus and try to feel what He felt when he said these same words. With the help of the Holy Spirit, try to identify yourself with His inner attitude of adoration, awe and gratefulness.