I think the easiest thing to draft for arenas is probably a weenie pally deck. Draft a lot of 2-3 cost minions, redemption, truesilver champion, etc. Get early board control (like turn 1 or 2) and attack him outright, try not to trade (unless it's a taunt) and let him trade into you. Playing this way, you should be able to finish the game before 8 mana, usually around 6-7 mana.
If you look at Day9's Blizzcon deck (below), you'll see the general feel of it. He doesn't do very well with it in constructed, but it's really strong in arena. Like I said, it's all about early momentum and making the opponent answer to your plays. Again, like all decks, if you get a shitty opening hand, you'll be boned for momentum, and likely boned for the entire game (which happens to Day9 in the videos below).
Another trick that's Day9 didn't do, but is pretty clutch, is to put blessing of wisdom on your opponent's minion. Preferably something with low attack and high hp.
