Unlock Heroes and the Arena
After clearing the Tutorial, which features six truncated matches against AI opponents, you can either play in Practice or you can head to the Play mode to face human opponents. The former option is your best bet, because you can determine the class of your opponent and the foes you face will generally offer less capable resistance. Once you play in Practice long enough to unlock each type of hero, you'll also unlock the Arena.
Unlock Cards by Leveling
You don't have to pay to gain access to additional cards. Each of the heroes has his or her own set of 20 basic cards (these are really only 2 sets of the same 10 cards). Defeating a hero in Practice Mode will unlock a few of the basic cards, and then the rest can be unlocked by leveling them up. Leveling up a hero is fairly simple. Just play any type of match: Practice, Casual, Ranked, Arena. Win or lose, the hero will gain XP good toward the next level advancement. Every few levels earned unlocks a new card.
Tips and Tricks
Quests Offer Great Rewards
While card packs and entrances to The Arena can be purchased with real money, they can also be purchased with the in-game currency - gold. Gold is earned by completing quests, and a few of the early quests will also earn a free Expert Card Pack.
After playing one match in Practice mode, the first quest should pop up, and it's a good one - play one match in Play mode (a casual or ranked match against a real player), and earn a free pack of cards. It's not necessary to win, just play.
From there, the next 2 quests are also relatively easy and rewarding - Play 3 games in Play mode to earn 100 gold (which is enough to buy another pack), and level any character up to 10, to earn a free pack. Once again, it doesn't matter if the games in Play mode are won or lost.
From there the quests get a little tougher and less rewarding, and they must be played in Play mode or The Arena, but they're still the key to earning gold. Most will have to do with winning games as a specific class of Hero, or defeating a certain number of minions, or dealing a certain amount of damage to heroes.
Craft Expert Cards
As you earn new Expert cards, you'll start to have a smattering of Expert cards across all the different classes of Heroes. A good way to make the most out of playing for free is to pick one or two classes to focus on, then craft some new cards for those classes. Do this by "disenchanting" the Expert cards from other classes, then using the Arcane Dust to craft new cards for the classes you want to focus on. It will take disenchanting higher level cards, or a lot of Common cards to make even one new Common card, but the advantage is you'll be able to choose exactly which cards you want to create.
Early Gold Investment Advice
Don't be tempted to spend the first 100 gold you receive on Expert Card Packs. Save it instead to go toward entrances to The Arena. Even if you lose, you'll still walk out with a new card pack and some Arcane Dust. Win a few matches and your investment will prove even more rewarding.
Proceed to the Arena with Caution
In the Arena, your opponents are human and your rewards can be significant. When you enter the Arena, after paying the 150G entry fee, you get to keep battling until you secure nine wins or three losses, whichever comes first. If you lose three times in a row on your first attempt, you'll leave with an Expert Card Pack and 40 Arcane Dust. If you win some rounds, your prize will be even better. For that reason, it's a good idea to get some practice before you enter the Arena, so that you can have a better time battling once you do enter and hopefully come away with better loot.