Arena

The Arena is one of the four game modes offered in Hearthstone. It was originaly named The Forge but it was changed to stop confusion over the name.
To gain entry to the Arena, players need to pay 150 gold (from Play modes and quests) or real money fee ($1.99/£1.49/1.79€). They must also have already unlocked every hero.
In this mode, players can put their skills to the test where deck-building is half the fun. Assemble a new deck by choosing from a selection of cards provided for the match, and then duel other similarly ranked Arena participants for a chance to win card packs.
You get to choose one out of three cards 30 times after choosing your hero. The cards you can choose from are randomly generated. You can get every rarity, even legendaries. After you have chosen your 30 cards you are ready to play. You cannot go back and change your mind about the card choices, so choose carefully!
You can play as often as you want with the deck. The deadline is 3 losses. The deck is "remembered" by the game, so players may take a break at any time. If you win your "Key" will be upgraded, up to twelve times. When you claim your rewards the key is used to open a Chest in an animation and you get rewards based on the amount of wins. The Rewards can be:

• A Card Pack

• X amount of Arcane Dust (not common above 10+ wins)

• X amount of Gold
• A Random Card

• A Random Gold Card (generally starting at 7+ wins)

Note that the rewards are not fixed per win; there is not a set reward for each key. Generally speaking players will make back their gold entry fee somewhere between seven and nine wins, and the gold/dust rewards exponentially increase.
If you lose 3 times, win 12 times, or retire, the deck will be "deleted" and you get your rewards. The better you did the better rewards you get.

Keys 

• Novice Key - 0 wins
• Apprentice Key - 1 win
• Journeyman Key - 2 wins
• Copper Key - 3 wins
• Silver Key - 4 wins
• Gold Key - 5 wins
• Platinum Key - 6 wins
• Diamond Key - 7 wins - From this point, you generally receive at least 150 gold and you can enter the arena right after you leave it.
• Champion Key - 8 wins
• Ruby Key - 9 wins
• Frostborn Key - 10 wins
• Molten Key - 11 wins
• Lightforge Key - 12 wins

Choosing your Hero 

With random card drafting in arena there is no way of guaranteeing card synergy. You will have to rely on luck and personal skill. Always choose the hero you have the most experience playing. Arena will put your skills and knowledge of a class to test against other players. If you are a beginner consider starting off with Mage or Paladin, if given the opportunity. These two heroes have amazing removals (Consecrate, Flamestrike) and good hero powers to keep up tempo.

Class

Class is the primary determinant of a hero's powers and abilities, and the strongest factor in deck selection. While each hero represents a unique character with their own personality, portrait and sounds, their class determines their Hero Power and which class-specific cards they are able to play. While each hero belongs to only one class, there are often multiple heroes representing each class. However, all heroes of a given class function identically, using the same cards and Hero Powers.
New players start with only the mage class available, and must unlock the others through defeating them in matches in either Practice mode or Play mode. Unlocking all 9 classes also unlocks various other game features: the Arena, adventures, and "Expert" difficulty Practice mode.

Hearthstone's classes mirror those of World of Warcraft. The current selection matches the class list from the original game, with classes added later not included, namely monk, death knight and demon hunter.

Druid - Malfurion Stormrage

• Shapeshifting protectors of the wild, with powerful Taunt minions and adaptable Choose One effects, druids are also able to accelerate their rate of mana accumulation, allowing them to surprise opponents with unexpectedly savage plays.

Hunter - Rexxar or Alleria Windrunner

• Trackers and huntsmen, with a synergy with Beasts, a selection of bows, and a supply of cunning deadly traps, hunters never miss their mark. Whether unleashing their Beasts upon the enemy or sniping them from afar, hunters possess relentless and immediate damage capabilities.

Mage - Jaina Proudmoore, Khadgar or Medivh

• Masters of arcane, fire and frost, mages wield formidable single-target and area of effect damage spells, and can freeze enemies in their tracks. Mages have a strong spell-synergy, capable of turning minor incantations into devastating Fireballs, and can employ a range of magical Secrets to redirect enemy effects, render themselves immune, or stop the deadliest foe or spell in its tracks.

Paladin - Uther Lightbringer or Lady Liadrin

• Stalwart champions of the Light, wielding sturdy weapons and gifting the recruits of their order with Divine Shields and a range of powerful Blessings. Paladins can also use Secrets to alter the stats of friends and foes, and protect vulnerable targets.

Priest - Anduin Wrynn or Tyrande Whisperwind

• Devout healers with powerful restorative abilities, capable of sustaining themselves and their allies while sweeping away enemies, priests boast a range of healing synergies, but can also rely on their darker abilities to manipulate and destroy enemies, peering into or even seizing control of their opponents' minds.

Rogue - Valeera Sanguinar

• Subtle and evasive assassins, using flurries of swift sharp strikes to slice and incapacitate enemies, rogues prefer to wield light daggers, laced with deadly poisons. Rogues prefer to assault their opponents in rapid bursts of activity, activating Combos to gain powerful additional effects.

Shaman - Thrall or Morgl the Oracle

• Masters of the elements, shamans command the service of mighty elementals, and even the Elemental Lords themselves. Shamans can Overload their mana in order to rise to the needs of the moment, with their attacks producing varying potency. Shamans can also summon Totems to boost their powers.

Warlock - Gul'dan

• Calling nightmarish Demons to their aid, warlocks are willing to sacrifice their own life and resources to send their minions hurtling at the enemy. Regarding their own lifeblood as nothing more than a currency, warlocks readily trade away their Health to draw additional cards, but must often pay a terrible price for the services of the infernal beings with whom they consort.

Warrior - Garrosh Hellscream or Magni Bronzebeard

• These lords of war use heavy weaponry and deadly attacks to slam and devastate the battlefield. While their skill with armor and shields allows them to soak up the mightiest of blows, their gladiatorial bloodlust brings synergy with Enrage and on-damage effects, sending their minions charging at the enemy.