What does this Mizmor discuss?
Rashi: It is about the future - "Ki Va Lishpot ha'Aretz" (13).
Radak (here and 105:1): David composed it 1 when he brought the Aron from Beis Oved Edom, together with Mizmor 105. This Mizmor is in essentially Divrei ha'Yamim I, 16:23-36; below (105:1-15) is Divrei ha'Yamim I, 16:8-22. For 43 years, they sang the former in front of the Aron in the morning, and the latter in the afternoon, until Shlomo brought it to the Beis ha'Mikdash (Yalkut Shimoni Shmuel II, 142).
Malbim: This and the next Mizmor discuss Hashgachas Hashem via nature, He does hidden miracles to save Yisrael, and for the success of His servants and lovers.
This is unlike Radak (91:1) brought from Shocher Tov, that Moshe composed all the Mizmorim from 90 until 101.
Who says "Shiru la'Shem"?
Radak: [A Yisrael] will say to his colleague, just like "Lechu Neranenah la'Shem" (95:1).
Why does it say "Shir Chadash"?
Rashi: This always refers to the future (refer to 96:1:1:1).
Radak: It is for gathering us from Galus. It is a new song, other than those written [in Tanach]. Those written are called Shirah (feminine), for they were for benefits that did not last; they were weak like a female. The future benefit (Ge'ulah) will be permanent; for it we will sing Shir - a male is stronger than a female (Shemos Rabah 23:11).
Malbim: Nochrim know that He is the First cause, but they thought that He is like other workers; when they finish a matter, it does not depend on them. After one makes a watch, it runs by itself. Really, Hashem is different. He created the world, and its continued existence is a constant creation. If He would remove His hand from it for a moment, it would revert to void. Nochrim sing an old Shir, that He created the world; you should sing a new Shir, that He renews the creation constantly.
Why does it say "Kol ha'Aretz"?
Radak: "Kol ha'Aretz" refers to all the residents, like "v'Chol ha'Aretz Ba'u Mitzraimah" (Bereishis 41:57). Malbim - now, most Nochrim deny Hashem. They attribute the entire creation to stars and Mazalos. (Then, all will admit to Him.)