Playing the Twilight Drake
You have a slight edge if you go second due to The Coin. You can use it on turn 3 to bring your drake out early, or wait until turn 4 and it'll act as an extra health point. In most cases, your drake will end up being a 4/5 or higher. The Twilight Drake's potency will be impacted by the type of deck you're using, too. Playing Twilight Drake in a heavy minion deck is almost a bad idea because your hand size will often be low as you're playing minions to overwhelm your opponent. Ideally, you want to play these in a more control-based deck like Mages and Shaman where you'll find yourself holding onto cards and reacting to your opponent's moves.
Playing against the Twilight Drake
While it is possible to go toe to toe against the drake in combat, it usually is a better idea to eliminate it with a crowd control spell. A Polymorph or a Hex will immediately neutralize it. Silence effects will remove the Battlecry and drop the health back down to 1 allowing you to send a weak minion to get rid of it. Also, while the drake will have a large pool of health, it doesn't have taunt. You can send your minions after it, but you might end up in a situation where the Drake takes down two or three of your minions before it dies. Shaman decks can easily deal with this by simply using Earth Shock. Read the wording of the card carefully: Earth Shock silences first, then deals 1 damage. So the Twilight Drake loses the health bonus from the Battlecry and then succumbs to the 1 point of damage.
All in all, a handy card to have for control users. It plays strongly with my Shaman control deck.