Hunters are the second most difficult kill for a Priest (course, I never have to fight Shammies, who I hear are vicious).
 

Hunters will always get the jump on you (unless they are stupid), and attack with the mana draining attacks while their pet feeds on you. It is important to close on the hunter as quick as possible. 

If he can keep you at range, you are dead, so get close. If you have the blackout talent, cast Shadow Word: Pain rank 1 repeatedly on the hunter as you close, until blackout proccs.  Hold your fear until you are in range of both the pet and the hunter, then fear, drop both your dots on him, followed by 2 dispels (his buffs) and Flay him once. After your flay is up run towards him. It can be effective to proc Touch of Weakness, then wand him since he is a high hit rate/low damage class.

When he comes out of fear, throw a shield up right in his face and Blast/Flay him. The secret is to stay so close to the hunter that he cannot use his rifle. If you have Improved Mana burn, sub that in instead of the Flay after the first fear, just make sure you are close to them when they unfear. Most hunters have short mana bars, and a single mana burn can tremendously reduce the hunter’s capabilities.

Finally, beware the big red pet hunters. Their pets are immune to fear and movement impairing effects.  Luckily, these hunters have invested so much in their pet, that they have gimped offense.  Charge the hunter, using SW:P 1 to proc blackout on the hunter, then dropping a real pain on them, and concentrate on surviving the 15 seconds the pet is “invincible”. As soon as the pet returns to normal, fear. At this point you should be able to kill both.

A shadow priest should beat a hunter 50% of the time.  A hunter will kill a holy priest 95% of the time.