In WoW, Priests can pose a challenge to a hunter. They have some of the survivability of a paladin minus the damage mitigation, but more DPS to back it up. The tactics for taking down a priest depends largely on their spec. Basically, if they are holy or shadow. A holy priest has moderate DPS, but can last a surprisingly long time for a caster thanks to their heals. Whenever possible try to keep your Aimed Shot's healing debuff up. A shadow priest can deal lots of damage, regenerate mana and has some nice damage mitigation.

Thanks to their fear and shield abilities both specs will have plenty of opportunity to heal themselves back up, so sustained damage is not worth while. Draining their mana can also be a tough challenge. While it is possible with a holy priest, you will rarely last long enough against a shadow priest to make a dent in their mana. Regardless of spec, your best option is to stay as far away from them as possible. Almost all priest damage spells are either channeled or require casting. So if you can keep ahead of them they won't be able to use their most powerful attacks. Buy wow gold can help you a lot with this game. 

When it comes to damage dealing bursting them down as quickly as possible, with a little bit of kitting mixed in, is the best path. First, send your pet in and have it go berserk. Use some of your powerful shots to bring them down and wait. If they feel desperate they may try to shield themselves or use their fear on your pet. If you have kept out of range though you should be ok. Like fighting a paladin, wait for them to use their shield and then take them out. Having Arcane Shot dispel their bubble will make the fight all that quicker. Without their defenses you should be able to burst them down quickly. Here is the cheapest WoW powerleveling service.