Psalm 110
This is a psalm about the messiah, about Jesus. Verse 1: “sit at my right hand”; verse 5: “the lord is at your right hand”. From verse one we see the Father talking to the Son. From verse five we see the Son talking to the Father. This psalm is about ruling, power and judgment. It talks of ruling in the present: "in the midst of your enemies"; and later, at the judgment and destruction of the enemies (vs 5-7). It shows that the Father chooses to rule through the Son and the Son rules to bring about the Father's purposes: “I and my Father are one” because he speaks of himself as ”the lord at thy right hand”
This psalm clearly shows the Father-Son aspect of the Trinity. Perhaps it does not show the Holy Spirit part because God doesn't want us direct our praise to the Holy Spirit. The Holy Spirit’s function (at least one function) is to guide us to all truth, to guide us to the Father and Son.
This psalm shows us the inside personal thinking that God does within himself. What a privilege that he shows it to us.