How to play a Holy Priest? Now we first talk about healer. As you know, playing a healer is a great fun if you are into being a support player. Be prepared for the role though as many players just can not sit back and not be directly involved in combat or damage dealing. As with playing any other healing class, you need to understand that while you rarely do anything to the enemy, you allow or enable your group to survive to do damage. This is not something everyone can cope with, so be warned.
If this is the type of character you want to play though, there are few better than a priest. Priests have huge heals, heal over times, instant heals, area of effect and group heals, shields and more. As if all your healing ability was not enough, you also have several utility spells, such as mind control and fear. Using all your abilities to the fullest will guarantee you invite too many groups over and over again.
For the most part, gear for healing is fairly easy to get and your main concerns should be +Healing, Intelligence and Spirit. Luckily all of these come in at least pairs on most healing items you will find.
By far, Intelligence and +Healing are the most important stats as they will allow you to cast more effective heals over a longer time that the other stats. To be truly effective you should aim to have at least a mana pool of 7000 and +1000 healing by level 70. If you focus on these stats you will also gain +Mana per 5 seconds, Stamina and Spirit as they are common on all the gear that has the other stats. While stamina is important so that you can take a hit, you will likely get enough while focusing on the other abilities that you will not have to hunt it out on your own. The same holds true for spirit and as long as you get some, you will be ok.
In PvP healing, you can almost completely ignore spirit as the fights will generally not be long enough to require it. However, in PvP you will need to focus much more on stamina and resilience to be able to take hits. If you are raid healing as long as you have enough stamina to absorb AoE and unavoidable damage, your end up spending a lot of effort on +Mana per 5 second and +spirit gear so that you have enough mana regen to last for long fights.
   The healing priority is making sure that you know when to keep people up, and when to let them die. There are situations such as the Mage or Warlock are doing mass AOE against a group that needs to die, or a single MOB being left at low health and a last heal being available for the tank or DPS or any number of other specialized situations. While it is important to stick to the priority as much as possible, you should learn to recognize when exceptions to it are important as well.
   In a fight, mana management is managing the amount you heal. It's possible to heal everyone as soon as they take damage and even to keep everyone at 100% health. If the tank is taking most of the damage and everyone else is just taking collateral damage from things, why heal them at all, unless they are below 50% health? If players are pulling aggro just because they know you will heal them, stop, make them learn aggro management. If everyone is above 80% why cast small heals, wait a while and regenerate some mana.
How heal needed and how much mana heal will cost are some things to worry about. It's better to cast many small heals, or wait until the player is lower in life and cast one big heal. Since big heals are generally more mana efficient, it is generally better to wait and cast a bigger heal. This is not always practical though, so you need to learn to judge.