So started playing WOW having never played this type of game before and think I'm getting there, as the quest side of things is pretty straight forward but decided to start doing some dungeons and arenas and I must be doing something very wrong.
In the arena, i seem to die as soon as someone even looks at me the wrong way, yet although I'm meant to be dps i seem to hardly scratch the other guys. I've got good equipment and the likes. I'm a lvl 28 fury warrior with two one-handed swords.
Same pretty much with the dungeons, they seem to be quite frustrating in that everyone just seems to run through full pelt so you struggle just to complete the quests or risk getting stranded, but again, as soon as an enemy targets me, I'm a dead man pretty much.
Is there something fundamental I'm missing?
Hi Jock, Defiant306 did a good job of answering your questions, but as a long time veteran of WoW Id like to chime in as well
Dungeons
WoW's group dynamic is based around 3 main roles:
1. Keeping everyone alive (Healing).
Pretty self explanatory - a Healers job is to keep everyone alive through their healing spells and abilities. Healers are limited by their mana pool which controls how long they can heal for, and their spellpower determines their healing throughput (HPS or Healing per second).
2. Taking damage from hard hitting monsters (Tanking). Tanks have the best "mitigation" abilities - High Defense and Armor. Therefore they are best suited to keeping the attention of monsters focused on themselves, and away from other, "squishier" characters such as DPs and Healers.
3. Dealing damage (DPS or Damage Per Second)
You mentioned you were a DPS warrior, so this will apply to you. Not all DPS players realise this, but as DPS you actually have two roles - dealing damage,
and absorbing as little damage as possible.
The reason is because monsters attacking low-defense DPS characters results in very inefficient healing by the healer. This will actually slow the group down, so as DPS it is your responsibility to ensure that you are attacking monsters that are firmly focused on attacking the tank.
In a 5 man group there will be 1 Tank, 1 Healer, and 3 DPS slots.
All that said, at your level a lot of this wont be an issue since everyone is going to be incredibly overgeared for the content. However, it is really good to keep the above in mind for when things get tougher later on.
So many DPS players end up dying because they get "aggro" from the tank, or attack too early on a monster. They then proceed to (wrongly) blame the tank and/or healer. Don't be this person

.
Battlegrounds
A system exists in the game that allows experienced players to equip their lower level characters with blue quality gear that actually scales with level. This is called heirloom or "Loom" gear. It makes them extremely powerful in lower bracket Battlegrounds, and as such they should be avoided by newer players until you reach the level cap.
This is really unfortunate, as Battlegrounds are enormously fun.
Anyway I hope that helps - take your time levelling as some of the content is very good!
