What does this Mizmor discuss?
Malbim: All the Mizmorim from here until Mizmor 100 discuss two conducts via which Hashem conducts His world - (a) Hashgachah via nature, and (b) miraculous Hashgachah, not via nature. This Mizmor discusses the difference between Yisrael and the nations.
What do we learn from "Lechu Neranenah la'Shem"?
Radak: In the days of Mashi'ach, a Yisrael will say to his colleague to sing to Hashem, who saved them. "Lechu" is not going, rather, making zealous to act. This is like "Lechah Nashkeh Es Avinu" (Bereishis 19:32) and similar verses.
Radak (91:1, citing Shocher Tov): This shows that Moshe said this corresponding to his Brachah of Yisachar, who engaged in the Rinah (song) of Torah.
Malbim: This is one of the two reasons to sing to Hashem - (Shem Havayah shows that) He created the world and all existence. Also refer to 95:1:3:1.
Why does it say "Nari'ah l'Tzur Yish'enu"?
Malbim: This is a second reason to sing to Hashem - He is the rock of our salvation, via Hashgachah Pratis. When the king comes among the nation, they sound a great Teru'ah - "Mah Kol ha'Teru'ah ha'Gedolah ha'Zos b'Machaneh ha'Ivrim va'Yed'u Ki Aron Hashem Ba El ha'Machaneh" (Shmuel I, 4:6), "va'Yari'u Kol ha'Am va'Yomeru Yechi ha'Melech" (ibid., 10:24). There are two ways to recognize Hashem and His Hashgachah. (a) From the Klal of the creation one sees that there is a Creator, the Cause of causes. Via this he investigates His particular deeds, how all are arranged with Chachmah, Chesed and mercy on His creations, and knows that He is Mashgi'ach and conducts His world. The nations recognize Him in this way; therefore, the verse tells the entire world to sing to Hashem. Also refer to 95:2:1:2.