How often do trading cards drop?
Typically you get one drop about every 15, 30 or 60 minutes of "gameplay" depending on the game.
By gameplay, of course, I mean "have the game running", and by "have the game running" I mean "the border of your avatar changes from blue to green." For example, for Trine 2, idling in the launcher counts as gameplay.
Hot Trine 2 gameplay action
From personal experience, it appears that you can get a drop every ~15 minutes so long as you restart the game after every drop.
From my experience, it depends on what game it is. For Terraria and Bastion, I noticed it was roughly every 30 minutes. With Surgeon Simulator 2013, I know I was in game for at least 45 minutes before one dropped. For FTL, I can't remember exactly, but I think it was somewhere from 30-45 minutes per card.
I'd be happy to try out other games and time them, if you want. There are a ton of games I have that I haven't touched since they started using cards, so I have all my drops.
"Most games will drop a number of cards equal to about half the number of cards in that game's set of cards."
"Free to play games drop game cards based on your in-game purchasing. For every $9 USD spent (approximate) since the start of the Steam Trading Card Beta, you will earn one card drop. This card will drop at some point as you play."
Now to answer your question: After reading 30+ user's comments on this question it appears to be that the cards drop randomly. While the game is running (you don't have to actually be playing it).
Also according to a user on steam: "The commonly held theory is that 1 booster pack is generated every time a badge is created. We're pretty sure it's not time based, but we don't have a lot of data so no one's certain."
Sources: http://steamcommunity.com/tradingcards/faq/ http://steamcommunity.com/groups/tradingcards/discussions/1/864971765638107405/