What approach should I take to DPSing as a Shadow priest?

Solution 1:

The short explanation is that you stay in Shadow Form 95% of the time, throw DoTs on everything, then sit back and watch the enemy's face melt. Remember that you can still cast Discipline spells, namely Power Word: Shield. The only reason to leave Shadow Form is to cast an emergency heal (or three, since they're going to be pretty wimpy as a Shadow priest).

DoTs

You learn three main damage-over-time spells, which are pretty self-explanatory:

  • Shadow Word: Pain
  • Devouring Plague
  • Vampiric Touch

If the enemy's face isn't melting fast enough for you, you can use Mind Flay or Mind Blast to speed things up. Once its health drops below 25%, finish it off with Shadow Word: Death.

You should be able to easily juggle multiple enemies at a time by casting DoTs on everything, then using Psychic Scream (or Dispersion) to keep them off you until they die. For me, this worked all the way through to level 80 where mobs started to get beefier.

Mana

Shadow Priests get a lot of mana replenishment abilities.

You'll definitely want to use Glyph of Spirit Tap, which replenishes mana when you kill an enemy using Shadow Word: Death, and Masochism/Glyph of Shadow Word: Death which replenishes mana when you don't kill an enemy using Shadow Word: Death.

Eventually you'll learn Shadowfiend, a temporary pet that gives you mana when it attacks, and Dispersion, which replenishes a bunch of mana and prevents 90% of damage for a few seconds.

Mind Spike

Once you hit level 81 you'll learn Mind Spike. Along with the Mind Melt talent, this gives you an alternate way to open combat: Instead of applying DoTs, you can cast Mind Spike twice then follow up with an instant-cast, guaranteed-critical Mind Blast which (with Paralysis) stuns the target for 4 seconds. If the mob isn't already below 25% health after that assault, you can just throw out another Spike or a Mind Flay before finishing it off with Shadow Word: Death.

Solution 2:

Holy damage spells are mostly for the healing priests to get them through dailies or as a burst option for healing PvP Priests.

As noted by Brant you should rarely ever leave Shadowform. If you keep Vampiric Embrace up and throw dots on anything that moves you whould be able to kill mostly anything without having to heal up. Also note that you should be using Shield regularly.

Also note that there are two ways to play a Shadow Priest in PvE leveling: Either through DoTs with Vampiric Embrace / Vampiric Touch / Devouring Plague and Shadow Word Pain or through Mind Blast and Mind Spike. It largely depends on your style of play. Although I found it more efficient to just DoT stuff and wait for it to die.

As for mana replenishment and DPS: Use everything you have (Shadowfiend, Dispersion, Hymn of Hope) on cooldown and you should rarely see downtimes for drinking.

Shadowfiend is also a great burst ability that will also give you a lot of mana. If there is a harder mob (elite) open with Shadowfiend while you DoT up and start the Mind-Flay spam until it's over (don't forget to re-apply your Dots).

Solution 3:

I remember lvling my priest. Shadow form is a huge dps boost when you get shadow form but it's a completely different play style. As these guys have said, you're in shadow form all the time - especially in combat.

For me, I always found myself burning through mana like crazy! I finally stopped using shadow word: pain and though it took a little longer to kill things, I'd open with Vampiric Touch, Mind blast then mind flay till they either died or reached me...

Hope that helps!