It looks like you can only spend real money to buy packs. That is obviously an error, since it would make your game incredibly hard to get into, which is EXACTLY what you should not be doing right now
Complete challenges to earn in game coins. Every day you can buy 1 pack with 3,500 in game coins.
As long as there is a free challenge slot, you get a new challenge every 2 hours, so log in once every 10 hours to clear your challenges.
Join a team/guild. Every 5 days team challenges reset. You often get 1 or 2 team challenges to win X games with a specific TOON. Then you get 3 packs. You can easily win these games in Trial mode.
Every level up you get 100 blue gems (the real money currency). So every 2 levels you can buy a pack.
Also, joining a team allows you to exchange resources with each other to build the materials for crafting specific cards.