'Rashi': When Shmuel ha'Ro'eh showed to him, like it says above "Yisad David u'Shmuel ha'Ro'eh be'Emunasam" (9:22). "B'Noyos ba'Ramah" - David and Shmuel were in Ramah, engaging in the Noy (beauty) of the world (the Beis ha'Mikdash - Zevachim 54b). He learned then more than a great Chacham can learn in many years (Midrash Shmuel 22).

Radak: He knew Tavnis ha'Bayis via Ru'ach ha'Kodesh - his own, or via Shmuel ha'Navi.

Malbim: Aside from the simple meaning, the entire Mikdash and its rooms hint to wondrous matters, both in the big world, and the small world (the Nefesh). Both of them are arranged like the Mikdash - the wise know this. Tavnis ha'Mikdash, and all its Chatzeros and chambers were in David's Ru'ach. Chazal expounded "Ki Vayis Ya'aseh Lecha Hashem" - David himself was like a picture of the Bayis above.