Cards are purchased from the marketplace option in the main menu, and you use them during the expeditions part of the game. There are five cards in a pack, and each pack costs credits to purchase.
There are a few ways to get credits, but you'll get enough for the achievement from completing challenges in the main game (Or you can can spend real world money for them if you're that way inclined)
Purchase the packs and flip all the cards over to see what you've won.
If you don't care about the cards too much, and just want the achievement, buy the bronze packs - 5000 credits. You'll only need around 120,000 - 130,000 credits, as the game rewards you with free packs of cards as you progress through the missions. (I know, that sounds like a lot of credits, but you stockpile them fast, trust me)
I unlocked this right after completing the story line. Once you've purchased and opened 30 card packs, the achievement should pop.