What is the meaning of "Asaprah El Chok"?
Rashi: It is a fixed statute; I accepted on myself to make it known.
Radak: David said, I will make this tale a statute and a custom.
Malbim: Just like there are laws for running the country, there are laws between nations. E.g. a king may not invade the borders of other kings and nations without a sufficient claim. If one breaches this and goes by force to destroy nations and steal their inheritance, he is called a tyrant. David said, when I conquer nations, I tell the law that Hashem gave to me. "The land and all in it are Hashem's" (24:1); He permitted me [to conquer nations], and made this a Chok. This is like the Midrash (cited in Rashi Bereishis 1:1), if the nations will call us robbers for taking the land of the seven Kena'ani nations, we will say that Hashem created the world, and gave it to whom He desires.
How did Hashem tell David?
Rashi: Via Nasan, Gad and Shmuel.
Why did he call him "Bni"?
Rashi: You are the head of Yisrael, who are called in the Torah "Bni Bechori", and they will endure via you, like Avner said "Hashem Amar
Why did He say "[ha'Yom] Yeladticha"?
Rashi: You are called My son, and dear to Me like a son due to them - "Ki Niseis l'Ma'alah Malchus Ba'avur Amo Yisrael" (Divrei ha'Yamim I, 14:2). We find that Jewish kings dear in front of Him are called sons. It says about Shlomo "Ani Ehyeh Lo l'Av v'Hu Yihyeh Li l'Ven" (Shmuel II, 7:14). It says also about David "Hu Yikra'eni Avi Atah Eli v'Tzur Yeshu'asi" (below, 89:27).
Radak: The day that David was anointed, Hashem took him for a son - "Li Melech" (Shmuel I, 16:1). That day he received Ru'ach Elokim - "va'Titzlach Alav Ru'ach Hashem El David meha'Yom ha'Hu va'Ma'alah" (ibid., 13). He said songs and Mizmorim with Ru'ach ha'Kodesh that entered him from Hashem. He received also Ru'ach Gevurah. "Tzur Yeladcha Teshi" (Devarim 32:18) - He raised you, and put in your heart Chachmah and intellect on the day of Ma'amad Har Sinai; "Hu Avicha Kanecha" (ibid., 6). "Yeladcha" and "Kanecha" cannot refer to physical formation, for Yisrael are the same as others! Hashem is also your mother - "va'Tishkach Kel Mecholelecha" (ibid., 18).
Malbim: Today the nations are agitated to rebel against David. Today Hashem made him a son to rule over everything, like a son who rules over his father's property - "va'Ani Nasachti Malki" (verse 6).