What does this Mizmor discuss?
Rashi: It discusses the world to come, which is totally Shabbos (Rosh Hashanah 31a).
Radak: It discusses the days of Mashi'ach, which are totally Shabbos (Rosh Hashanah 31a).
Malbim: It discusses Hashem's Hashgachah in His world. It looks like everything is based on nature, but one who is wise will see His Hashgachah - punishment of Resha'im and reward of Tzadikim. Hashem hid His Hashgachah from the masses, to leave room for choice.
Who composed this Mizmor?
Why does it say "l'Yom ha'Shabbos"?
Rashi: The Leviyim said it [in the Mikdash] on Shabbosos. Also refer to 92:1:1:1.
Malbim: Shabbos is the testimony of the conduct of Hashgachah; the world is not left to nature and chance. Therefore, this Mizmor (which discusses Hashgachah) was established for Shabbos.