To use the new Grouping System, you have to be lv15. To use this system, once you are 15 just press the "i" button and click "Join".
It will put you in a random Dungeon that you are able to run at your level. At the end (when I say end, I mean the last boss, or the boss you have to kil to get the bag. Some bosses may get skipped) you will be rewarded with a Bag that will have some kind of item that should be useful to your class.
Your role as a Hunter is Range DPS. You send your pet into the fight as melee DPS and you stand in the back with the Casters (or even father back) and pewpew at the target (being low level you don't have as many skills to use, apply Serpent Sting, use Arcane Shot). Make sure you have full control over your pet. You don't want it running around attacking things, and do make sure you turn off Growl while in a group.
You pretty much shoot the target like you have been while soloing.
At lv15..I don't remember what the Dungeons are. I know one is Raging Fire Chasm (RFC), it is a Horde dungeon but thanks to the new system Alliance can be placed in it. It is a lv 10-15-ish dungeon so I'm sure you will land in there one or 2 times.
Some dungeons HAVE quests for them. The use of this site or other (wowhead, wowwiki, thottbot) can inform you on what quests there are and how to go about and get them. Some quest you will not be able to do. Take RFC for example, even tho Alliance can now get into it. All the quests for the Dungeon are Horde based.
You can Grind dungeon, but once you kill everything inside (or mainly the bosses, as they are the ones who drop the loots) most will leave the group. The new system pairs you up with people from your Battle group (Realms are put into Battle Groups. It is like 6-10 Realms per BG). Once the group has left you can just re-in list to join another.
Some dungeons are easy and quick. Some are long and rely on everyone paying attention to what is going on.
Edited, Mar 9th 2010 9:04am by Sandinmygum