Generally speaking, a Priest hangs back and furnishes a shield spell, heals and dispels to primary attacking group members with the occasional offensive assist. Most groups do not expect a priest to engage in a lot of direct combat, since they are often the best healers. If you have wand and heal and shield are not immediately needed, shooting your wand is a good way to assist doing damage without getting directly involved and allowing your mana to recharge at the same time. It's best to target the target of the MT to do your wand damage to, because one, their aggro is likely firmly on the MT, and two, concentrated damage, rather than spread out damage (i.e. everyone focuses on one mob) takes down enemies faster. Depending on group makeup and skill, dropping a DoT like Shadow Word: Pain on as many mobs as possible at the beginning of the fight makes mana-efficient sense, but be sure your group knows how to hold aggro on all of them, or you'll get a surprise after the first tick of damage.
   In the group, the Priest, as the primary healer should be prepared to use an array of healing spells from the instant cast heal over time Renew to Flash Heal, Lesser Heal, Heal, Greater Heal and/or Prayer of Healing in the group. For Priest, the key to group survivability is effective mana management and the use of healing in the right situation. Casting a three seconds heal when the player has 2 or 2.5 seconds to live is a mistake many inexperienced priests make. Better to cast a quick small heal or two followed by a longer heal, than to hope you win the race casting the larger heal.
In term of casting time or mana cost, many Priests make use of an escalating ladder of heals. It's vital that the Priest continuously monitor the health bars of party members and be aware of the rate at which they are taking damage. The main tank may have the most health, but be taking damage from the entire group of mobs and require most of the priest's attention. On the other hand, if a mage ends up drawing the aggro of a mob, the mage may go down quickly if the priest isn't able to pop a quick Flash Heal and/or shield on them. A Priest's situational awareness is essential to preventing a wipe. It is better to have everyone in the party finish a fight with only 10% of their health than to lose one or more members. At least, a player with 1% health fights just as well as one with 100% health, so the survival of the maximum number of party members will always be better than preserving just one. However, the most important person to keep alive (if you must choose) is the MT, as, once they die, the mobs aggro almost invariably turns to you, the healer. As usual, this results in a wipe.
For the most part, you should get to know the fact that healing can generate aggro. The bigger the healing, the more aggro the Priest generates. A Priest must always try to maintain the delicate balance of providing the right amount of healing without generating too much aggro or wasting too much mana while ensuring group survival.