Here are some things I've learned about zealots that I think are valid, at least up to level 23. I'm specced in the Witchcraft line btw so some of these things may be different for other mastery specced players.

Please feel free to add to this or argue points.

But first, one thing you can do regardless of which class you are playing, is to place yourself between the enemy and the friend being attacked by the enemy. I've used this many times in capture-the-flag type scenarios to stop someone that is chasing the flag carrier. The collision detection doesn't always work, but occasionally it does and lets your friend get out of range.

There are two main rules I've found so far for playing a zealot.

1. Don't Panic!

Zealots, and probably most healers, are very hard to kill. The trick is to realize that the npc or player simply can't kill you (unless he's a bit higher level or has a friend). Obviously this may change at higher levels but so far it is true.

2. Have patience.

Killing anything, particularly other players, is going to take time. In fact, if the enemy player has any sense, they'll run away once they realize that they can't kill you, which means you probably won't kill them either.

For example, yesterday I killed a champ +2 levels over me. It wasn't particularly difficult but it did take nearly five minutes. I've also been attacked a couple of times by equal level tanks and melee-dps in PvP and found that they couldn't kill me but I could slowly wear down their health. Again, this may change at higher levels.

Other general tips (some may be obvious): 

Pay attention to your Action Points (AP), they can drop quite fast. Doing damage is fine but stick to heals if your using AP too quickly.

Don't forget the abilities gained from your buffs and remind group members to use them. (I don't think they use any AP either)

Heal Over Time (HoT) spells are the zealots strength but you have to remember that they heal OVER TIME so casting them when someone is nearly dead probably won't save them. You can try casting your damage absorbing spell on them prior to or immediately after casting the HoT so that it has a little time to heal, which does work if the person isn't taking damage too quickly. But it's safer to cast the shield, do an instant direct heal or two, then apply a HoT or two.

Unlike healers in other games, it is usually better for zealots to try and keep everyone close to full health. If someone takes damage, dump the instant HoT on them. In PvE it doesn't seem to cause much aggro.

If you are outclassed in a fight and have some friends around (in PvP/RvR) you can sometimes brush the enemy off by moving behind your friends. Sometimes the collision detections works and the enemy gets stuck on your friend preventing the enemy from being able to reach you.

The Harbinger doesn't seem to do much by itself and takes a lot of AP but it may be worthwhile if you have some abilities that require it.

You get a group heal spell that works as long as the group member is within a certain range. It does NOT require line of sight, which is great when you are in a group that doesn't stay together or in an area with a lot of things blocking your lines of sight. The downside is it takes 3 seconds to cast.

Some sorcerers expect you to keep them alive even though they are constantly causing massive damage to themselves. Tell sorcerers in your group to discharge their magic energy once in a while. Trying to keep a sorcerer alive while he keeps exploding every two seconds will drain all of your AP leaving none for the rest of the group and the sorc will die anyway.

Melee-dps players are dangerous. I mean friendly ones, not enemy ones. Sometimes they get overconfident when they have a healer with them and start pulling huge numbers of mobs, which is ok except that you may be forced to cast a heal on them before they've caused damage to all of those mobs. If that happens you will almost certainly draw aggro from every mob he hasn't hit yet, which means everyone is in trouble.

Even when I was specced in the mastery line that improved direct-heal spells, they didn't seem very good, which is why I tend to think that HoTs are our bread and butter.

My typical attack steps:

PvE - Doombolt (one or two), instant DoT,  AoE DoT, instant Direct Damage (DD), instant HoT, Bolt, instant DD, etc..

PvP - instant HoT, instant DoT, AoE DoT, buff DoT, 2 sec cast HoT, recast each as needed. Other spells too depending on situation but that's generally what I do.

I think there were other, and better, tips but I'm tired now and can't remember them.

-Moldyjoe