I've settled on a Priest of Mitra as my main character and the person I play with is playing a Dark Templar. Fairly standard duo stuff, the eponymous tank and healer.
The benefit of this set up is it makes it very easy to form groups which is just as well because even though the server is busy it is not easy to form groups in AoC. The UI doesn't help much at all.
There is a group tab in the UI. It allows you to search for groups and even restrict your search to an instance. So I can search for level 30-35 groups inside the Black Castle. The flaw however is that these are full groups, midway through the adventure, not partially formed groups recruiting players.
There is also a LFG channel which makes a good starting point for building a group and which occasionally presents you with a forming group for an instance you're interested in.
The way I build groups is I ask my friend who I'm on skype with, I then ask my guild and friends list, then I ask in the LFG channel and finally I do a Player search for level appropriate players and send everyone tells. So far everyone I've sent an unsolicited tell to has either not responded or been polite so don't worry about doing it - people are generally glad to be asked and don't get asked that much.
You need a tank, which to me is a Soldier class player who wants to tank. You will sometimes find a dps-specced Soldier who will reluctantly agree to tank, that's usually a recipe for disaster. Tanking is pretty hard and the dps-specced tanks can't take the hits.
You need at least one healer, preferably two. Healers of different classes stack better so a Bear Shaman and a Tempest of Set will give you better healing than two Priests of Mitra. This is because one of the hots can be run concurrently with another classes minor hot so if I run my Emanation of Mitra heal over time a Bear Shaman can run her Renewal where a second Priest could not contribute a second Emanation.
Healing is a matter of keeping your heals going while nuking. In a twenty second cycle I will cast my two heal over times and have an emergency big heal to cast if things look grim. Otherwise I can nuke and luckily the Priest gets a talent allowing one of my nukes to give a minor secondary healing effect. Every little bit counts! The spell is called Lance of Mitra.
You'll notice the name is vaguely phallic. Like so many things in Age of Conan there is an undercurrent of double entendre which both deliberately and accidentally fills the game world with hilarious moments. It's like Arnie meets Frankie Howerd.
DPSing in Age of Conan is an intense affair of aggro management. You have to watch what the tank is doing and not start early, hit the mob he's not focussed on because if you rip aggro it's very hard to heal you. This is because most healing is directional and pointed at the tank. Unless you happen to be standing next to the tank the heals won't hit you. The healers can recast the heal to hit you if you stand still or if the healer correctly hits you on the run but that's really hard to do.
It's actually very skilled, challenging and fun. It also creates comical Benny Hill chases as the dps runs from the mobs who are chased by the tank who is chased by the healers.
The instances are fairly trash-intensive. Patrols often come along moving at high speed and can add before you know they are there. Ranged pulling and corner pulling is recommended.
Trash doesn't seem to respawn in the low to mid level dungeons we've experienced so far.
Bosses are often rather more complex than simply tank 'n' spank. The last boss of the Pyramid of the Ancients for instance is only beatable if you perform the correct sequence of buffs using items dropped from 4 previous bosses. The sequence is Shadow, then when boss life is 75% Holy, then when boss life is 50% fire, then when boss life is 25% Frost. The last boss in the Black Castle in an endurance test against waves of multiple adds. Gathering them close for AoE is really the only workable strategy unless you out-level the instance.
All told it's very fun to get into groups even if it's a little cumbersome to organise. Best to be about 4 levels higher than the instance claims to be as they're super hard at the correct levels in a random group.