Power Word Shield and Fade
In general don’t use your shield unless you have to.
It costs 600 mana and so in a 10 minute fight you could waste 6000 mana with no gain if your not attacked!
If you pull aggro pop Fade ASAP and be ready to shield if it wasn’t enough to reduce aggro (fade usually works except when the tank is dead and then your screwed anyway). Some bosses/mobs hit for way more than the 1.5K or so dmg the shield absorbs so Fade is far more effective at avoiding max dmg. Sooner you hit it sooner the mob should return to the tank (I have it below my Mind Flay button for easy access).
Shield and ShadowWord: Death
If you’ve shielded up and not taken any hits that mana was wasted. When the Weakened Soul debuff fades (15 seconds) use ShadowWord: Death. Your shield will absorb the vast majority of the dmg caused to you from the ShadowWord: Death. Even with a crit the worst case scenario is 1.5-2K dmg which is easily regained with Vampiric Embrace (imp Vampiric Embrace is useful here) and a few Mind Flays.
Same technique can be used when you have Prayer of Mending on you. It can absorb well over 1K of the ShadowWord: Death dmg and passes the Prayer of Mending to another raid member.
When I do arena I use Prayer of Mending, shield myself, go shadow form and mount up during the countdown phase (time it so mounted just as the arena starts). Run into the arena and hit a target with ShadowWord: Death for no dmg to me (got to use ShadowWord: Death within 10-15 seconds though otherwise the shield has gone).
Shadow Priests Dealing with Aggro
To allow a tank to gain aggro start with VE, Vampiric Touch and ShadowWord: Pain (if still moving VE, ShadowWord: Pain then stop to do Vampiric Touch). This will keep you low on the aggro list with little reduction in dmg. Better to do less dmg per second and survive the entire fight creating mana and health for your group than pull aggro early and die just to be high on a dmg meter.
If you see a non tank gain aggro stop casting immediately and wait for the tank to regain aggro. Since the tank isn’t hitting the mob, if you continue to do so you could easily pass the tanks fading aggro and die a few seconds later. If you see the mob go to a second caster hit fade because you might be next. DO NOT cast a spell until the tank is back in control (unless it’s a DPS race to finish Leotheras the Blind for example during enrage at 1% ). Amazes me how many people continue to DPS when a tank looses aggro!
If you do manage to grab the aggro and fade fails do not run away, if your not sure where the tank is stay still, shield up and hope the tank regains aggro in time. If your sure where the tank is run to him/her. Worst thing you can do is run away, makes it harder for the tank to regain the mob.