No, its not possible to 'earn' any card. If you own Skyrim, you'll get 4 cards of the 8 available (completely at random, potentially including duplicates.) After that, there are 3 ways to get more cards: buy it on the Steam Marketplace, trade for it with another player, or hope you'll get a booster pack. There's nothing you can do to get a booster - they become available when people craft badges, and are then distributed randomly to players eligible for them. They're extremely rare, and again, no guarantees on what would be in it, even if/when you get one.