After a few horrible LFD groups I've decided to put together a short guide for people using the Random Dungeon Finder, primarily aimed at level 15-30 characters.

I will deal with each of the party roles in the order: Tanking, Healing and Damage dealing.

So I want to be a tank
For a sart, I must be a Druid, a Warrior or a Paladin; please tell me that iff you have a Death Knight you don't need to read this!
What do I do? I get all the hostile creatures (mobs) to attack me, instead of my more fragile fellow party members.
I do this by holding threat, also known as aggro. Creatures always attack the character with the highest threat, so I want to make sure I am generating more threat than anyone else in the group.
Healing and Dealing Damage also create threat, so I have to be alert to what my fellow party members are doing.
So I'm going to take a pounding
As a tank, I need to be able to take a lot of hits before I die, or the healer will not be able to heal me. How do I make sure I survive.
There are three ways to survive being hit.

 

• lots of hit points, so I can survive being hit more often
   
• a high armor value, so I take less damage with each hit
   
• the right talents: this makes a really big difference after about level 30, but is too complex an issue to deal with now.
  At later levels I also need
   
• avoidance stats: dodge, block and parry, which allow me to be hit less often

To get more hit points I need as much stamina on my gear as possible.

Roughly, at level 15, you should not try to 'tank' with less than 500 hit points
The starting stats I need as a tank vary by class
 

• Druids: Stamina and Agility and wear all leather armor
   
• Paladins: Stamina and Strength and wear all mail armor (plate after level 40) and a shield
   
• Warriors: Stamina and Strength and wear all mail armor (plate after level 40) and a shield
   
• Death Knights: if you have a death knight you really shouldn't need a guide like this. you start in appropriate gear for BC instances from starting area quests

Part II
So I want to Heal
I must be a Druid, a Paladin, a Priest or a Shaman.
What do I do?
I heal the party when they take damage. First and foremost, I have to stay alive myself. Then, I have to make sure the Tank stays alive. If I can, I also make sure the DPS stay alive. Remember, if you heal a DPS, but the Tank dies, you might all die quite soon afterwards. If you heal the tank and a DPS dies, then you can resurrect the DPS afterwards.
What's my most important resource?
My most important resource is mana. My current mana is indicated by the blue bar under my green health bar.
I get mana directly from intellect. I regenerate mana faster based on my spirit.
Therefore, the two most important stats on my gear are intellect and spirit. It's better to be a paladin in cloth with high intellect and spirit, than wearing leather or chain (or plate) with no bonuses to these stats.
What else?
Your spells heal for more the more spellpower I have. This is based mostly on intellect, but some items (mostly weapons) give pure spellpower.
what do I need?
Intellect and spirit. It's that simple. As long as I'm wearing gear giving me bonuses to these stats, I can heal.
I also need the right talents. After a certain stage it becomes impossible to heal effectively without the right talent tree chosen no matter how high your spell power, intellect and spirit may be.

Part III
So I want to Deal Damage
I could be from any class. If I'm a Hunter, a Mage, a Rogue or a Warlock I don't have a choice in the matter. This is the only thing my class is capable of.
People might think I'm useless, but in many ways I'm doing the most important job. I have to kill the enemy before he kills the tank, or the healer runs out of mana.
What's the biggest thing I can bring to the party?[b]
Attitude. I shouldn't endanger the party by rushing ahead of the tank, as this might lead to a wipe. I shouldn't demand that the healer heal my pet when the tank is taking a pounding.
[b]no but seriously, what cool things can I do?
Actually, I can do lot's of cool stuff. The most important abilities, aside from dealing damage are Crowd Control.
A rogue can sap, A mage can polymorph, an enhancement shaman can hex, etc. etc.
Using these abilities can make a huge difference when the party is facing seemingly overwhelming odds.
but what do I want on my gear?
This varies by class.
 

• Paladin, Warrior: strength is our most important damage dealing stat
   
• Enhancement Shaman, Feral Druid, Rogue, Hunter: agility is our most important damage dealing stat
   
• Druid (Balance), Priest, Mage, Warlock, intellect is our most important damage dealing stat.

Agility increases attack power (amount of damage you deal with your weapon) more for some classes, and critical strike rating for all clases.
Strength increases attack power more for some classes than for others.
Intellect increases both spell power and spell critical strike chance. It is the stat of choice for any spellcaster who wants to deal damage.

That about wraps up my advice.

I've tried not to go into too much detail, as this is meant to be a guide to the basics those people who want to level using the RDF system.

Most of all, don't be afraid to ask. For all you know, the level 15 gnome rogue in your party could have a realm first Kingslayer title on his alt, and he might be able to tell you everything there is to know about your class.