What separates arena from constructed is a lack of specialized decks. There are no aggro decks that only run small, cheap creatures, and there are no control decks that run lots of board clears and few creatures. Everyone runs a sort of midrange curve-out deck with high creature counts. What this means is that and anti-creature cards, like unconditional removal and sweepers, will always have a good target. It also strengthens buff spells, like blessing of kings and dark iron dwarf, because your opponent will always have a minion for your buffed guy to trade into, and because low spell counts make it hard for an opponent to finish off a guy that you buff and trade with so that it lives on low health. Finally, it makes it difficult for a player to come back if they're behind on board, since the player who is ahead on board gets to dictate creature trades, and the low number of sweepers make it hard to reset a board where you're behind. This means that it's important to play to the board early, and it's important to have ways to finish off minions that live on low health after a favorable trade.

Priest's hero power is very strong if you're ahead on board, and very weak if you're behind. If you're ahead, you can attack your large guys into your opponent's guys, and then heal them, but if you're behind, it doesn't do much of anything, and you have no way to finish off low-health enemy minions, so if you fall behind on board, it's hard to come back. What this means is that priest wants to play big minions that can survive until they untap and get healed, like 5 mana 4/6s. Cards that are weaker in priest are those that you can't heal, either because they're split into multiple smaller bodies (e.g. infested tauren), because they have low health,
or because they have divine shield. Strong class cards are health buffs, removal, area of effect, and creature stealing.

Mage is probably the best arena class at playing from behind. Your sweepers are stronger when your opponent is ahead on board, and your hero power and burn spells let you finish off opposing minions after they trade into your slightly smaller minions. Cards that are better in mage than other classes are enrage cards like amani berserker, which can be activated with your own hero power, cards that synergize with mage's high spell count, like violet teacher, and elementals or cards with elemental synergy, like firefly and tol'vir stoneshaper, because mage's class elementals make it easier to draft elemental synergy decks. Strong class cards are area of effect, removal, and random spell generation.

Warlock can fall behind on board and lose very easily. Your hero power doesn't affect the board, and if your opponent puts you to low life, you can't even use it. A strong way to play warlock in arena is as a zoo-style deck, where you play a lot of cheap minions on curve, and lifetap when you have 2 free mana or when you're running out of cards in hand. Getting ahead and staying ahead on board will preserve your life total, and keep your opponent from getting favorable trades that leave them with damaged minions you can't finish off. Warlock also puts a premium on taunt minions and lifegain, because your hero power lets your turn your saved life into cards. You should avoid expensive cards because your hero power lets you win lategame anyways. Strong class cards are removal, sweepers, and 1 drops.

Rogue is similar to warlock in that you pay life to use your hero power. Like warlock, you want to get a fast start to preserve your life total, and put a premium on taunts and healing. Unlike warlock, your hero power is a lot better early because it gives you a lot of tempo. Activating hero power on turn 2 is a better play in rogue than any other class. Cards you want to take highly are the powerful rogue removal spells, and weapon synergy cards like silithid swarmer and spiteful smith that work well with your hero power.

Hunter in arena follows the same principle as hunter in constructed. You play cheap, early minions, push damage to the face, and get them low enough before they can stabilize the board that you can finish them off with hero power. Like warlock, your hero power doesn't give you any tempo, so it's better to develop minions than use hero power until you start running out of cards to spend mana on. Beasts and beast synergy cards, like zoobot, are stronger in hunter than in other classes. Strong class cards are weapons, removal, beasts, and beast synergy cards.

Paladin gets a lot of small guys off of its hero power.. Cards like abusive sergeant and cult master that let you leverage these small guys for value are stronger than usual in paladin. Strong paladin class cards are weapons, buffs like spikeridged steed, and handbuff cards like smuggler's run. Buff cards let you immediately eat an opponent's creature, and have a big damaged minion left over. If you get handbuff cards, it can be worth building your deck around them by avoiding spells and maximizing your minion density to maximize the number of cards you get buffed.

The main things you need to play around against priest are health buffs, like power word:shield, sweepers (holy nova dragonfire potion), and minion borrowing effects like potion of madness and shadow madness. Clear their minions whenever you can so they can't buff their health, eat your guys, and heal them, and don't play minions into a board you're already far enough ahead in that they need a sweeper to come back.

The two things you need to play around against mage are sweepers and secrets. To play around sweepers like blizzard, volcanic potion, and flamestrike, don't extend small minions onto a board you're already far ahead in, and trade your small minions that die in sweepers for their minions. Play around meteor by positioning your biggest minions on the edges of your board. When playing around secrets, try to figure out whether it's a minion secret, a spell secret, or a face secret.

Minion secrets are mirror entity and potion of polymorph, which trigger when you play a minion. Check for them with a cheap minion or a battlecry minion, and play your minion before you make attacks so you trade into a mirror entity with the minions you have on board.

Spell secrets are counterspell, mana bind, and spellbender, which trigger when you play a spell. Check for them with cheap spells or with the coin. Remember that if a secret isn't triggered by a spell that doesn't target a minion, it could still be spellbender.

Face secrets are vaporize, ice barrier, and ice block, which trigger when you go face. Check for vaporize by attacking with your smallest minion first. You don't need to play around ice barrier, but checking for it can let you know it's safe to play other minions. Ice block is rare in arena, but if you suspect your opponent has one, try to get them as low as possible before triggering he block.

Finally, if your opponent plays an elemental on turn 6, they're probably going to cast blazecaller next turn.

The main things you need to play around in warlock are are sweepers. The warlock sweepers are dread infernal, abyssal enforcer, felfire potion, twisting nether, doom, shadowflame, and hellfire. Play around them by not overextending into boards you're already far ahead on, and by trading your small minions that die to sweepers for their minions.

Swipe. Swipe swipe swipe. Don't get swiped. They also have starfall, and they can blow you out with buffs like mark of the wild, mark of y'shaarj, mark of the lotus, and power of the wild, or just kill you with savage roar. But the important thing is not getting swiped.

Rogue has a lot of hard removal in vilespine slayer, assassinate, and envenom weapon. Generally, playing more than one small minion to bait out removal is better than playing one really big minion in the lategame. They also have fan of knives and betrayal, so trade in your 1 health guys and watch your positioning.

Volcano, flametongue totem, lightning storm, maelstrom portal. Also, remember that they can roll healing totem when you're doing your combat math.

Nobody plays warrior. Don't get brawled.

Paladin has equality, consecration, lightfused stegodon, secrets, and buffs like blessing of kings, blessing of might, divine strength, dinosize, and spikeridged steed. You can play around buffs, stegodon, and equality by keeping their board clear, and you can play around consecration by not having a bunch of low health minions at once. The 4 main secrets are getaway kodo and redemption, which you want to trigger by killing a small minion, noble sacrifice, which you play around by how you sequence your attacks, and repentance, which you want to trigger with a small minion.

Hunter has explosive shot, grievous bite, deadly shot, unleash the hounds, and secrets. You play around explosive shot and grievous bite with positioning, you play around unleash by not having a wide board with lots of low health minions, and you play around deadly shot by playing 2 medium guys instead of one big one. As for the secrets, you play around explosive trap and misdirection by not going face when you have a board that's vulnerable to them. You play around freezing trap by attacking with a small minion first. You play around cat trick by playing minions instead of spells until you've stabilized the board. Don't try to play around snake trap, it's an epic and "never attacking enemy minions" isn't really a viable strategy against hunter anyways. There's also hidden cache, but there's no real way to play around that.

It's generally a good idea to keep the other side of the board clear, because of neutral cards like dark iron dwarf and stormwind champion that let your opponent make favorable trades if they untap with minions. It's also worth remembering that corrupted seer and primordial drake are neutral sweepers, meaning that any opponent could have them.