A few resources to encourage your understanding of the Psalms.
Listen and watch David Murray explain briefly how the Psalms help us to sing to Jesus (as well as the Father and the Spirit), of Jesus, and with Jesus.
Tim Challies has a good reminder of why Christians can join David in singing as he did in Psalm 119, "O, How I Love the Law!"
In a catechism-style format, Pastor Brad Johnston has a helpful new book called 150 Questions About the Psalter: What You Need to Know About the Songs God Wrote.
The Bible Project released the video below with its vivid, engaging diagram that explains the structure of the Book of Psalms. The picture that emerges helps identify several important themes pointing to Christ that are carried through the Psalter. (Note: One error that somehow it maintains is that the Book of Psalms is not a hymnbook.)