Can I get some cards for free?

Solution 1:

Aside from the 10 packs you start with when you purchase the game, the only way to get more is either to buy them with real money, or to play Expert Gauntlet games and win 4-5 games (or 3-5 in Keeper Draft, but you need five packs to play that mode, as well as two Event Tickets). Your initial game purchase also includes 5 Event Tickets, which gives you five chances to win additional packs.

After you exhaust the packs and Event Tickets that you start with, you have to buy more from the store. You can also buy individual cards in the Marketplace.

Finally, you can Recycle unneeded duplicate cards to get Event Tickets, to try your luck at more "free" packs, and sell Uncommon/Rare cards in the Marketplace to effectively trade for more cards.

Source: Official FAQ