Aggro decks are the most difficult to handle since an aggro deck can quickly establish board and deal lots of damage through spells, which are both hard to counter in a deck with only a handful of minions.
Start of Game
Early Game
The early game can be controlled with spells like Potion of Madness and Shadow Word: Pain. Power Word: Glory is also an effective counter when cast on an enemy minion because it allows you to heal 4 health to negate or minimize incoming damage.
Midgame
Once an aggro starts to fill the board cards like Excavated Evil and Mind Control Tech come into play.
Late Game
Since an aggro will likely have few to no large minions, the late game can either be handled by either swapping decks using King Togwaggle to turn your opponent's deck against them, or if your opponent is within lethal range (10 health) you can use mind blast to deal the final blow.