Well there's not much point discussing the different classes without mentioning specific cards they have, so I'll list a few that are notable for each class.
Shaman: Storm Shock, Lightning Arc, Fork Lightning, Earth Shock
Rogue: Purloin, Stab in the Dark, Carnage, Thud, Surge of Adrenaline
Shaman AND Rogue: Daggers eg Perdition's Blade, Black Amnesty and Retainer's Blade
Druid: Cyclone, The Natural Order, Stormfire, Form of the Serpent
Warlock: Hesriana, Eye of Kilrogg, Banish to the Nether, Steal Essence, Drain Will
Warrior: Puncture, Vindicator's Brand, Keys to the Armoury, Pummel. Weapons in general is what the Warrior will be interested in
Warlock AND Warrior: Bloody Ritual
Priest: Melt Face, Mists of Corrosion, Mental Anguish, Divine Spirit
If you want more specific deckbuilding tips, decide what kind of deck you want to build first (aggro, control, ally-based, equipment-based etc). Then you can decide which class will do that best.
If you're interested in the kind of aggro deck I mentioned above, Shaman and Warlock are good. There was an article about "Battle Lock" not long ago which covered an aggressive Warlock deck, and Kilzin (aggro Shaman) has been around for ages.

Props to darknesspwns for the sig
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