Booster packs are randomly dropped to people who have run out of card drops of a certain game. The more badges people craft, the higher the chance of you finding a booster pack - it will literally drop a notification on your steam to let you know you found one, and it will contain 3 cards for one game.

Trading is a different story, you might have to visit individual game forum discussions on Steam, or find a trading community. That, or you can buy or sell extra cards through the community market for like, 15 - 30 cents. Kind of a weird system, but that's how it works right now.

Hey, I just got your message - You get XP by crafting badges on Steam, and you get badges by crafting Trading Cards together, and you get Trading Cards by playing select games. See what badges you have a chance at making by hovering over your username next to community and selecting "Badges" on the pull-down menu.