For most games that have Steam trading cards, you earn cards by purchasing and playing the game, for which you will receive 1/2 the cards in the game's set (rounded up).
Free-to-Play games operate differently. You instead earn card drops by spending money, either from that game's in-game shop or by buying the game's DLC in the Steam Store. The current rate of all Free-to-Play games is approximately $9 US per card drop, but it is believed that Valve can adjust the rate on a per-game basis (though no games currently appear to be using any other rate).
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