The general game plan is taking your opponent to fatigue or using N'zoth as a win condition.
Quick mulligan guide -
Rogue, Hunter, Paladin, Mage - Keep Reno Jackson, consider shuffling quest and try to find AOE spells, Sludge Belcher can stick for a turn and save games!
Warrior, Priest, Druid, Warlock - As these decks are usually playing control lists, mulligan for powerful swinging cards such as Kazakus and Emperor Thaurissan as they can be difficult to play around so might force awkward trades and board states. Remember not to waste removal and don't worry about taking too much face damage because of the huge healing potential. If you included weapon removal, look for it early as it can be a huge game-winning card in some matches.
Shaman - Very difficult if playing against Shudderwock, go for early sticky minions such as Cairne Bloodhoof and Piloted Shredder. Make sure to go face where possible as trading may put you behind.
Mind Control Tech if aggro becomes an issue.
Dragonslayer if facing lots of Dragon Priest's.
Harrison Jones or Acidic Swamp Ooze to help against dude paladin or cubelocks
Golakka Crawler helps with pirate warriors and dragon priests using Nightmare Amalgam
Zola the Gorgon -> Baleful Banker or Youthful Brewmaster.
Emperor Thaurissan -> [High value / Swing card], for example, Kel'Thuzad.
Lightbomb -> Psychic Scream or Excavated Evil.
Radiant Elemental or Lyra the Sunshard -> Priest of the Feast if more healing is needed.
Cairne Bloodhoof -> Piloted Sky Golem or another sticky minion for control matchups.
Excavated Evil could replace lightbomb if aggro is an issue.