Be up front and ask questions. If you zone into a dungeon you're doing for the first time, say so. A simple "first time in here" will let other players know that you're still learning the mechanics of the instance and may need guidance. It's always possible that an impatient member will drop group or, worse, vote to kick you, but trust me: You don't want to go through the dungeon with that person anyway. The vast majority of groups will be relieved that you spoke up and will offer information throughout the zone. When you come to a boss you haven't seen yet or don't remember, a quick "Does this guy do anything special?" should be enough to get the tips you need. If none of your group members are forthcoming, you'll have to rely on general dungeon knowledge to get you through.
Know your CC. If you're a DPSer, make sure you know all of your class's crowd control options and have them ready in a convenient place on your action bars. If you're a tank or someone who is leading an instance, it's probably a good idea to be familiar with all crowd control options, but if you're not, ask the group who has CC at the beginning of the dungeon. The person leading should assign a mark to each CCer and keep the assignments consistent throughout the run. If you are a DPSer who has a useful CC ability but the tank is forging bravely ahead, speak up and mention your capability. It could mean the difference between an easy pull and a trash wipe.
Get DBM. The Deadly Boss Mods addon is an essential tool in any dungeoneer's arsenal. If you're quick-witted or a veteran of other WoW dungeons, DBM's announcements will help you know what to do even if you've never seen the dungeon before. Healers will especially appreciate the announcement of special boss abilities, as these almost always cause the group to take more damage and a heads-up can help the healer compensate. DPS will be warned not to stand in the fire and when to interrupt boss spells.
Don't stand in bad things. As we all know, if the floor changes color at the boss's behest, it's time to move your butt and get to a safer spot. Fire, shadow, falling rock, water, arcane magic -- all of these are examples of Things You Don't Want To Stand In. Most players are pretty good about not standing in the fire, but it's important that you keep your eyes open, even on trash pulls. Don't overwork the healer's mana by being slow to move. Also, melee DPS especially should be aware of the mob's proximity abilities. If you're standing in front of something that is hurting you, move out of the way.
Stand in good things. Cataclysm has introduced a new dynamic to the old not-standing-in-fire strategy: good fire. Some of the healing classes have gained new AoE heal abilities that show up as spell graphics on the ground -- but these are the good kind. If your healer casts one of these spells, such as Efflorescence, Power Word: Barrier, or Healing Rain, it'll show up as a shiny spell graphic at a fixed location. If it's possible and convenient amidst your other responsibilities on the fight, move into these spell graphics so that you benefit from the AoE heals.
Watch your health. If you're not the healer, it's important to watch your own health. If you notice that you're taking a lot more damage than usual, you may be standing somewhere you shouldn't be. Awareness is key. It's also a good idea to have potions, bandages, or self-healing cooldowns ready, but do not use them unless necessary. Cataclysm healing is not about keeping players at full health, and if you use your self-healing abilities when you are not in immediate danger of dying, you're just wasting the healer's mana; he or she was probably in the middle of healing you.
Follow the leader. If you're the only one new to the dungeon, chances are the other players know things about the encounters that they've either forgotten or neglected to tell you. If you see everyone else moving to a certain spot, moving out of a certain spot, or switching DPS to an add, be the sheep and follow along. Awareness is still key! It could save your party from a wipe.
All of these tips notwithstanding, it's still a good idea to read a guide for dungeons you have yet to visit. WoW Insider has some great guides up for you to peruse, and it doesn't take long to give them a once-over. However, if you zone into an instance and draw a blank, these tips will help you make the most of it. Good luck and have fun!
World of Warcraft: Cataclysm has destroyed Azeroth as we know it; nothing is the same! In WoW Insider's Guide to Cataclysm, you can find out everything you need to know about WoW's third expansion, from leveling up a new goblin or worgen to breaking news and strategies on endgame play.