A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 96:1The substance of this Psalm, and portions of the ninety-seventh, ninety-eighth, and hundredth, are found in 1Ch. 16:7-36, which was used by David's directions in the dedication of the tabernacle on Mount Zion. The dispensation of the Messiah was typified by that event, involving, as it did, a more permanent seat of worship, and the introduction of additional and more spiritual services. Hence the language of these Psalms may be regarded as having a higher import than that pertinent to the occasion on which it was thus publicly used. (Psa 96:1-13)
All nations are invited to unite in this most joyful praise.
new song--literally, "fresh," or new mercies (Psa 33:3; Psa 40:3).
psa 96:2show forth--literally, "declare joyful tidings."
salvation--illustrates His glory in its wonders of love and mercy.
psa 96:4For He is not a local God, but of universal agency, while idols are nothing.
psa 96:6Honour and majesty--are His attendants, declared in His mighty works, while power and grace are specially seen in His spiritual relations to His people.
psa 96:7Give--or, "ascribe" (Psa 29:1) due honor to Him, by acts of appointed and solemn worship in His house.
psa 96:8offering--of thanks.
psa 96:9beauty of holiness-- (Psa 29:2).
fear . . . him-- (Psa 2:11).
psa 96:10Let all know that the government of the world is ordered in justice, and they shall enjoy firm and lasting peace (compare Psa 72:3, Psa 72:7; Isa 9:6-7).
psa 96:11For which reason the universe is invoked to unite in joy, and even inanimate nature (Rom 8:14-22) is poetically represented as capable of joining in the anthem of praise.