How do I pick up trading cards?

Ah, I found my answer at the verrry bottom of the Steam Trading Cards FAQ:

Do I get Trading Cards for completing achievements in game?

Trading Card drops are currently just tied to playtime within a game, independent of which achievements you are getting. We will definitely look into adding more rules for how cards are dropped in the future, but there are a few problems with in-game achievements that prevented us from using them right now. Many games have achievements that are grindy or un-fun to get, and we want the act of getting game cards to be fun for all users in games. We also don't want to push users to cheat or use achievement-unlockers in games in order to get cards, since that devalues achievements and isn't that fun either.

To confirm, you can indeed just go to main menu and wait for +/- 20 minutes. But of course it is more fun to acually play the game.