People leveling World of Warcraft warlocks have always had to choose between Affliction and Demonology to level from 1-80. Affliction relies mainly on the warlock, and the damage over time spells (DoTs) while Demonology relies on your pets taking damage and keeping you safe. Many players will choose to level with Demonology as it is the safest path to leveling a warlock to level 80, but Affliction is the fastest path.
Upon closer inspection you will see that Affliction allows you to rapidly cast a number of your DoTs on your target, while still maintaining some longer casting time spells. This can be used to your advantage in many situations. For single target fighting you will lead with a rotation such as:
Unstable Affliction - With it being a longer casting time, you will not fight pushback casting it to lead.
Start running away - Keep your distance for a bit, your next three spells are instant casts.
Cast these spells in any order - Siphon Life, Corruption, Curse of Agony.
Either keep running away, or stop and cast Drain Life until the mob dies.
Generally you will not have to reapply any DoTs as the mob will die quickly. At higher levels you will replace Unstable Affliction with Haunt for the heal effect. If you are getting hit hard, fear your target and continue to cast Drain Life.
Single target fighting is the weakest aspect of an Affliction Warlock. Where they shine is fighting multiple mobs, due to the nature of the DoTs.
To pull off Affliction speed killing you need an area ripe with mobs, a DPS or mana pet (Succubus or Imp respectively), and some guts. You do not need as many mobs as an AoE grinding Paladin or Mage, and a little distance between pulls is a plus. Optimally you will want to control four to six mobs at a time.
The rotation is simple, rely on your instant cast spells and dps pet to do your damage, while fearing the mobs if you get in trouble. Simply Curse of Agony, Siphon Life, Corruption, tab to the next target, and repeat. Generally I pull 4-6 targets then cast an instant cast Howl of Terror and then Drain Life any that may still be alive.