you will find all answers here: http://steamcommunity.com/tradingcards

and i will write short version:
By playing games* you earn cards, if you complete whole set and craft cards, you will earn badge and get few extras:

a random emoticon item created for the game you can use in chat or discussions;
a random profile background item created for the game that can use on your Steam Community profile
a chance to get a discount coupon for a different game or DLC
100XP, which may increase your Steam Level

There is only 1 problem. You alone can get only half of full set by playing game. So you need to get rest of cards from other ppl (who don't need them).

Cards price depend on title. The cheapest are cards from TF2.

*
CS:GO
Team Fortress 2
Dota 2
Portal 2
Half-Life 2
Don't Starve

http://steamcommunity.com/tradingcards/faq/

How can I get trading cards?
You can get trading cards by simply by playing one of the participating games. As you play, you'll occasionally receive trading card drops which will be placed in your Steam Inventory.

Is there a limit to how many trading cards can drop?
Most games will drop a number of cards equal to about half of the number of cards in that game's set of cards. For example, Half-Life 2 has 8 cards in its set, you can receive 4 card drops by playing it. You'll need to collect the other half of the set from other community members. Try the beta group discussions, community market, barter with friends, and trade discussions. You can check how many drops you have remaining on your badges page

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