Just to be clear, the trading cards don't actually do anything, right? Just... collectible graphics?
Steam Trading Cards.
-Games may or may not support trading cards.
-If they support trading cards, they will have a # of card drops available. Once these card drops are consumed, they are gone forever.
-The card drops are periodically received by having the game run, even if you aren't actively playing it. (In my experience, ~1hr between drops)
-You may receive regular cards or foil cards. You may also receive duplicates.
-You will never get all of the cards for a given game going only off of drops.
-If you have all of the cards for a given game, you can combine them into that game's Steam badge. If you have foils of all of the cards for a given game, you get a foil badge.
Steam Badges.
-Completing a badge gives you XP to level up your Steam profile. You may also receive things such as trade-able emoticons, special background graphics for your profile, etc.
Steam Profile.
-When you level up your profile, you may receive items, such as game price reduction vouchers, emoticons, backgrounds and trading card booster packs.
-The higher level your profile is, the more eligible you are to randomly receive booster packs. You enter to win a booster pack by logging on sometime during the week.
-Experience for profile levels increases every 10 levels. Levels 1-10 are 100 XP (One badge's worth), while Levels 11-20 are 200 XP (Two badges' worth). Beyond that, I don't know. The highest level (worth getting, anyway, I don't know if it goes past this) is 50, which doubles your chance to receive a booster pack every week.
That's about everything there is to know about the trading cards, badges and Steam profiles. Except you also get some other stuff for leveling up your profile, but it's weird, like increasing your friends list limit. I didn't know they had one. *shrug*
I've seen foils go for 90 cents up to just short of $3. I've seen regular cards for as low as 8 cents and all the way to 30 cents. By selling cards, I made enough money to craft enough badges to get to level 10, buy a cheap game, and still have some money left over.
Also, I've only ever gotten two booster packs. One was from leveling up (I'm pretty sure it was anyway), and the other was winning one randomly. It seems to be pretty darn rare on a personal level.