1. Shadow Priests are very efficient at Soloing.
They can kill the mob in very short time without consuming too much mana. But they are incapable of dealing with multiple targets and Elite enemies, team with other players if you need to deal with such kind of missions.
2. Deal with one mob each time:
The mobs in world of warcraft are well spread, and the agro between each other are not closely connected. So pull as less mob as possible for each combat. Better deal one mob each time. Beware of patrols, when you kill a mob and patrol comes, you have to face two of them, and the damage that you suffered could be doubled. In that case, you can pull the patrol and kill him first, then kill the targeted mob. In short words, avoid sudden.
3. Start attack from the longest distance:
Priest has many ranged attack skills, start from the longest attack range. For Melee mobs, they have to run close to you, this takes about 3 seconds. You can cast one or two more spells on him. In that case, he will only remain 70% HP then, you can kill him more easily.
Pack yourself up before leave the camp. Find blacksmith or Weapon Vendor to repair your gear, buy Sacred Candle from vendor. Don't forget to buy supplies such as Healing potions, Bandage, food and water.
5. Healing Gears:
Remember to have healing gears in your bag, no matter what spec you are. When your teammates need you, put up you healing gears. Healing is not only an ability but also responsibility.