Newer Systems since Wrath of the Lich King era:
The Dungeon Finder was already covered above, but you may have noticed some other functions on there:
Scenarios and Raid Finder.
Scenarios
Scenarios are basically the answer to dungeon queues sucking if you're not a healer or tank. In MoP they sort of replaced Dungeons in terms of grindable content for currency (which are going away so I didn't really mention them, sorry). Basically it's only 3 person, and there is no need for roles - the mechanics are all avoidable so DPS can do them you just can't screw them up as much. Think of it like Guild Wars 2 dungeons, only not completely terrible. The basic Scenarios are available as soon as you hit 90 and they won't drop particularly exciting loot, you may want to do them just to see them. Once your ilevel is up to 518 you can do Heroic Scenarios, which are VERY good Valor:time spent (The best in the game by far), and are moderately challenging - they emphasize having decent DPS and NOT MESSING UP MECHANICS. I wouldn't call any of them hard, but if you stand in things you will die horribly. These have a chance once per day to drop an epic item and are worth doing when you're gearing up.
The Scenario system is also used for lots of solo storytelling stuff, if you visit the Isle of Thunder you'll find many solo scenarios, and in Warlords there are no longer 3 person scenarios (there are twice as many dungeons instead) but there are LOTS of solo scenarios. They're a really strong storytelling tool.
Raid Finder
I'll make a longer raid oriented section later, but for now just know that there are LOTS of raid difficulties now, and Raid Finder is the bottom feeder one. Each zone has a specific required ilevel to queue (and I'll mention it now, you can see your item level on your character sheet under the general tab), and each one has to be done in order within the zone. For instance, Throne of Thunder is only one raid, but in Raid Finder it is split into 4 wings. Those go linearly, but the ilevel for queueing is the same accross all four. If you're casual, this is where a lot of players are content to spend their days, loot is individual per player and random. If you're a Brewmaster Monk you will only get loot appropriate to Brewmaster Monks, and you'll get something probably 10-15% of the time. Otherwise you get gold. The loot here is lower level than the actual raids on any difficulty, but it is otherwise the same. Mechanics are mostly intact but either sharply dumbed down or very forgiving of failure, and there is usually a lot of hilarity the first few weeks of any given raid tier as most of the people who have no idea what is going on figure out the 'hard' bosses (There's always something that ends up being tuned incorrectly and is a total roadblock in LFR the first few weeks).
Actually, raid section right now
Raiding!
Ahh the best part of wow (I'm totally unbiased). This is nothing like it was in Vanilla or BC. In Warlords it's not going to be anything like it was in Wrath or Cata or MoP either.
If you haven't played since Vanilla/BC: Raids are no longer 'farm all week, go in and wipe to the 20 morons in your group'. In Wrath they introduced 10 man and 25 man of the same raids (In Bc they were different, you may remember ZA or Karazhan for instance). The 10 mans there were strictly easier, and dropped a slightly lower quality of loot. In Cata, they decided to balance 10 and 25 to be 'equal'. Without getting into which is harder, the truth is either way it was never completely balanced, and some fights are harder on 25 (most of them) while some are harder on 10 (few of them). No matter what there wasn't Parity. It also really stifled raid design to have to make fights scale between such different compositions of players. In Mists, the raid size is going back to unified...sort of.
Currently you have LFR, detailed above, Flex, Normal, and Heroic. Flex is new, flex is easier than normal, but VASTLY harder than LFR. Flex also scales dynamically from 10 to 25 players in a raid. You can bring 13 people and have it scaled relatively appropriately to your group in terms of all mechanics. Loot drops according to the difficulty you're raiding on (regardless of raid group size): LFR, Flex, Normal, Heroic. There are also randomly Warforged items which are slightly better, to keep you coming back for more.
In Warlords, this is going to become LFR, Normal, Heroic, and Mythic. This is just a naming change. LFR will be exactly as it is now, Normal in Warlords is what is currently Flex. It will remain flexible. Heroic in Warlords is currently Normal, and it will now ALSO be flexible. Mythic is the new 20 person fixed size 'hardest' difficulty. It's analagous to heroic now. 10-25 split is gone, there is only 20. Warlords is also going to add more randomization along the lines of Warforged gear, there are going to be random secondary stats that you can get on an item (including tier this time), to make it so that there's almost no possible way to actually get a full best in slot setup. Gearing will never get completely stale.
If you haven't played in a while, things you might not understand about raiding in general:
- It is NOT easier than Vanilla/BC. It's vastly harder if anything. The low end of LFR and Flex is not challenging, but the hardest content has only gotten harder because of this split, not easier. There are only 2-3 bosses in all of BC that can compete with the challenging stuff they put out today.
- It is probably more casual friendly, but only in the sense that you don't have to farm for mats and garbage. It just takes a trip to the auction house to have enough potions, food, and flasks for weeks on end of raiding. Because of this you can now be a high end raider and maintain a normal life. Yes, the VERY top guilds poopsock, but you can raid 9 hours a week and barely play outside of that and still finish all of the hardest content before the tiers are over.
-There is an in game group finder tool (Not matchmaking, but actual LFG tool) they just recently added that should be more fully fleshed out for Warlords, to assist wtih making groups for the non-random stuff, like Normal or Heroic raids. There are also more sophisticated tools out there to make it easier than ever to find groups. Openraid.eu or openraid.us is a good start.