In groups you will virtually always be the designated primary healer. You will have little chance to do any significant damage other than wand blasts between heals. During the easier early fights of an instance you may be able to cast Shadow Word: Pain on some mobs.
Generally, you will spend the entire time healing. Being an effective and efficient healer takes a bit of practice, but if you know the basics, it becomes a lot easier. I will divide this section into 2 parts to deal with healing as you level, and healing at 70, because they can be very different.
Healing As You Level
Most of your instance groups as you level to 70 will be what are known as pickup groups, with people who advertise on the general or looking for group channel. These groups will often be comprised of jerks, newbies and morons. They will also often have a less than desirable class makeup. If you get in a bad group with one of the above, bail out as soon as you can. You are better off trying to find a new group, and generally it’s pretty easy as a priest. During most of the game, Greater Heal can be used as your primary heal on tanks. The monsters in the non end game instances generally don’t hit hard or fast enough to facilitate the need to use Flash Heal. Renew is also a fantastic heal to use in these situations on both your main tank or any other party members who take AoE damage during a fight, or if the tank loses aggro momentarily to another party member.
Using Greater Heal requires some timing and some trust from your tank. The advantage in using Greater Heal over Flash Heal is mana efficiency. To use it effectively, it’s best to wait till your tank is at about 60% of their maximum health. You can then start to cast Greater Heal. By the time casting is finished, your tank should be at about 50%. The heal should then return him to full. Play around with the numbers a little, but that is a general rule.

Prayer of Healing is another important spell for any priest. Priests are the best primary healers for group play because of this spell. It costs a bucketload of mana, however, and should not be used in every situation. If a mage or rogue gets aggro and takes a small amount of mana, and then the tank regains aggro, you should not use Prayer of Healing. When fighting a boss with big AoE damage attacks, like the Maraudon Princess for example, Prayer of Healing should be used. The general breakpoint for Prayer of Healing is 3 people to full health. If there are less than three people who are going to be fully healed by the spell, it’s better to use Flash Heal. It’s also important to know that Prayer of Healing creates a significant amount of threat because of the amount of health healed. This is a good spell to use in combination with Inner Focus if you have that talent.
Healing At Endgame
In the end game instances, especially the raid encounters, strategies have to change. Greater Heal is too slow to be an effective tank heal. You will need to spam Flash Heal on the main tank to keep him alive when he is taking damage in the thousands per hit.
For example, Onyxia has a flame attack that deals between 3 and four thousand damage, in addition to her standard attacks. That kind of damage coming at short intervals cannot be effectively counter through Greater Heal.
During the long battles in raid instances Meditation becomes an extremely valuable talent to have. When you are chain casting Flash Heal, you will have no time to stop and regen some mana. While only 15%, Mediation will allow at least some mana to regen while you are healing.
In any instance the most important person to keep alive is the main tank. If a mage or a rogue takes aggro off the tank, it will cost significant mana and cause high threat to the priest to keep them alive. In some situations it can be better to let the other members die.

This does not mean don’t heal them – throw up a Power Word: Shield, and a Flash Heal, but don’t keep casting Flash Heal over and over again. Explain to your members what happens when you get threat (they all die) and try and get them to go a bit easier on the DPS next time. It can help prevent a wipe. It’s much easier to res 1 person than to have everyone travel all the way back to the instance portal and then through the instance to where you left off.

The key to many of the end-game encounters is effective strategy. You need to know where to place your tank, what mobs to use crowd control on, and where to go. Don’t worry, much of it you will pick up on your own.
Healing And Threat
Healing threat is what gets priests killed. If you have a tank that can’t hold aggro effectively, you will end up attracting the mobs to you, and dying. A priest can take few hits before death.
Basically, healing threat is based on amount of hp healed. This means that a tank will have to do some damage to a mob to generate hate before you can heal them. For this reason, it is not a good idea to have a tank that is more than 2 levels below the highest level mob in an instance, because they will just miss far too much.
Healing vs damage equates to around 50% with the subtlety talent. What this means is that your tank will have to do around half as much damage as you heal to hold aggro on a target.
Overhealing does not add additional threat. What this means is that if your target is at 50/100 health, and you heal for 1000 health, you have only created 50hp worth of threat.
Your tank will have to do roughly 25 damage to maintain threat. (These are only example figures, obviously). Certain abilities like Sunder Armour (for the Warrior) create large amounts of threat. Try and get your tank to use these as often as possible. Heal over time spells, like Renew (and First Aid if you choose to take it) create threat on each tick of health, not initial or at the end of the duration. This is generally a better way to heal, as it means a tank can create threat over a period of time.

Power Word: Shield, which is very mana inefficient but a great lifesaver, actually creates less threat for the caster than healing for an equal amount. It’s roughly half as much threat to use Power Word Shield than an equivalent hp heal on a tank. This becomes even more effective when not specced with Silent Resolve. Contrary to what some people say, Power Word: Shield is applied after armour, so it’s good to use on high hp classes, and it also does not affect Rage generation of warriors in any significant way.

This means that it is a good idea to apply a shield before a big fight to act as a buffer. Fade is rather complicated in the way it works. It appears to reduce a set amount of aggro from the priest immediately. It should generally remove a mob from you from over- healing, unless you have a very poor tank and have been doing significant heals to more than one person. Threat from healing is still generated while fading. It doesn’t appear to be reduced, either, which makes the usefulness of the Improved Fade talent questionable. If Fade does not remove a mob, it means you are in big trouble. The tank will have a hard time pulling the mob off, especially with your desperate efforts to stay alive. The best way is to just cast Power Word: Shield on yourself and hope the tank can do his job.

As long as you don’t do anything right before Fade expires, you should not regain aggro afterwards. That includes Renew. The first tick of Renew after fading can bring that big hitting mob straight back to you, so be careful how you use it, especially on your tank.