Killing stuff as a shadow priest is rediculously (yes my spelling sucks, deal with it) easy, IF you picked the right talents. The savior of a low lvl priest, who misses the true power of Mindflay and PW:P (which doesn't really show till lvl 26 with Shadow Weaving and Vampiric Embrace) are 5 talents, not in the shadow tree, but in the Disc tree;
Wand Specialization; 5/5 = 25% more damage with wands
A good wand is all a priest truely needs to lvl like hell.
PW:P > Mindflay > Mind Blast > Wand till death.
Renew every third mob should help with the healing, untill you get Vampiric Embrace
Now, a couple of things;
1) Fear > PW:S
Not always, but often. When the mobs don't agro each other, its cheeper to fear the mob your fighting then to Shield (use Rank 1 Fear though); mobs don't attack you, you waste less mana, etc etc.
2) Spirit > Intelect
Spirit is a must; from lvls 30 > 60, I was able to grind without ever losing more then 50% mana before I logged (sessions of 2-3 hours); Spirit Tap is your best friend. Stock up on Spirit (the chest piece from Gnormeregan is... amazing. + spirit heaven)
3) Groups > Soloing
Your a priest. Priests can heal; EVEN shadow priests. Use it; the xp groups give in instances is way better then soloing (most of the time, anyway) and the gear you get helps.
Have fun lvling a shadowpriest, their awesome, and good fun. Just remeber; Shadow Priests can heal; don't waste bandages! Instead, give them to poor warriors!