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The role the priest must take in any group is the
healer and buffer. Priests should be able to keep everyone in the group buffed and healed at all times. Lets take a quick look at all the skills that really matter and how you will use them to become an effective group healer..
Soul Source – This is one of your 'holy crap' buttons. For whatever reason if your entire group starts taking a large amount of damage you are going to want to use this. You have to be picky when using it though because it has a 10 minute cooldown. The neat thing about this spell is that it consumes none of your mana and will restore your entire party's health to full.
Wave Armor – You are going to want to save this for your tank just before he pulls a group and refresh it when it fades. It lasts 60 seconds or until it absorbs a certain amount of damage depending on how high of a level you have it. Wave Armor can be thought of as a tool to help you save mana. If your tank doesn't take damage you don't need to heal and you can regen mana faster.
Healing Salve – Temporarily increases the amount you will heal your target for by a considerable amount, lasts 60 seconds. This is another one of your abilities that will require constant refreshing. If you have it at a high enough level all of your heals on the buffed target can heal for 100% more than usual for a full 60 seconds.
Regenerate – Also known as a HoT, Regenerate will heal the target over 20 seconds. The amount that is healed per 2 seconds depends on the level you have it at. Typically its a good idea to constantly have this on anyone taking damage unless you are having mana issues.
Urgent Heal – A 1 second cast time that will heal your target for a moderate amount. You should be using this heal if your tank, or any other party member, is low on health. It is your fastest heal so don't be afraid to toss some around at any time.

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Heal – With a 2 second cast time it really is not a good idea for this to be your main spam heal. However, your target has both Wave Armor and Regenerate then you could probably get away with a 2 second cast without anyone dying. It's a slow heal but its a big heal and it should be used when ever a party member is below about 30% health.
There are a few other heals that are available to the priest and you are encouraged to find ways to use them. The five I listed above, if used under the right circumstances, is all you will really need to be a successful healer.