Psalm 96 has no title in the Psalter, but almost all of it also appears in 1 Chronicles 16, in the song of thanks sung when the ark was brought to Jerusalem in David's day. It opens with a triple call: Sing to Yahweh a new song! Sing to Yahweh, all the earth. Sing to Yahweh! A new song fits a new act of God's salvation, and here the whole earth is the choir.
The psalm sets Yahweh against the gods of the nations: For all the gods of the peoples are idols, but Yahweh made the heavens. The Hebrew word for idols sounds like a word for worthless things. Then a second triple call echoes the first: Ascribe to Yahweh, you families of nations, ascribe to Yahweh glory and strength. Ascribe to Yahweh the glory due to his name. The nations are not only told about God; they are invited to worship him.
The climax is a message for the world: Say among the nations, Yahweh reigns. The world is also established. It can't be moved. He will judge the peoples with equity. All creation celebrates: heavens, earth, sea, fields and trees. God's coming judgment is pictured as joyful, because he will judge the world with righteousness, the peoples with his truth.