When does a card count as being played?

A card counts as "played" when it finishes the entire play process — meaning it finalizes and its resolution completes (Rule 350.1). Permanents hit that point when they leave the Chain and enter the board; spells when they finish resolving and go to the trash.

A few important edges: a countered card is never considered played (Rule 425.1.b), and "when you play" triggers fire at that completion moment (Rule 419.4.a). Hiding a card doesn't count as playing it, but flipping and activating it from hidden does (FAQ 2559). Repeat only plays the card once no matter how many times its instructions execute (Rule 746.3.a).