In order to receive Steam Trading Cards, you must play a game for some period of time. Is it possible to keep the game open as you go run errands, and have the cards when you get back, or do you have to be actively playing the game to receive cards?
Yes, you can. And since it's not mentioned in any of the other answers: there is even software that will iterate through your games, idling in each one until you get all the cards.
It's called Idle Master.