So you REALLY want in on a raid? Follow these easy steps!
1) Level to 80, decide on a relevant spec, learn ability rotations to maximize tanking/dps/healing
2) Get all of your gear at least in blues (this is not as hard as it sounds).
3) Buy/craft any relevant epic BoE items (rings, robes, etc). This is expensive, tedious, and time consuming.
4) Run heroics to replace blues with epics
5) …?
6) PROFIT!
Step one is easily a solo task, I can give you links to forums to discuss perfecting your role/spec/rotations.
Step two can be mostly solo via quests, crafting, and AH purchases. Five-man normal dungeon runs are good too.
Step three is downright tiresome. Earning reputation, grinding out mats, grinding up cash… it all pays off but it's tedious. Generally there is a weapon and a chest piece you can craft somehow. Rings and necklaces are good too, those craftable epics are some of the best in game currently.
Step four is where you really start to learn instancing/raiding. This is preferably done with a regular team of folk that are competent, patient, and reliable. Be sure to wear a tabard for a faction that has gear you want. There's usually an epic helm/glove/weapon/offhand waiting for you at Exalted.
Note that I frown on regular PUGing. This is because your group composition is never the same and there's no guarantee on thier skill. You won't know subtle things like how Bolsh always drops a thunderclap and shockwave after charging, so you time your sheeping until AFTER that. Ya dig? Bring pugged people INTO your group, test them out and if they suck drop 'em. If they're good friend them, run with them again and again.
Set guidelines on how loot is distributed beforehand, particularly if there's a choice item you are aiming for. Don't be afraid to set master-looter to yourself, nothing is worse than having a hunter roll need on that cloth bracer you're dying for.
As a DPS class here's some rough entry-level requirements. Mind you this is single-target sustained dps:
• Normal Instance: 800-1000 dps
• Heroic Instance: 1200-1800 dps
• Normal Raid (10-man): 1600-2200 dps
• Heroic Raid (25-man): 2000-5000 dps
If your output is anything less than that you become a liability. Most bosses have enrage timers, thus it's either a DPS race to bring it down or a mana dump race to beat it before your healers are tapped out.
Sometimes other folk in your group can make up the difference for lagging dps, but there should still be a minimum TOTAL dps. For instance, to bring down Patchwork or Thadius in 10-man Naxx you need at least 15,000 total dps. Fall short of that and it's just a long walk to a wipeout.
Other advice? Hrmm...
Know your class inside and out. Know what abilities to use and when. Always keep your self-buffs up (Molten Shield, Inner Fire, Battle Shout, etc). Know what abilities synergize with other classes - such as Priest's Devouring Plague adds to a Death Knight's overall dps because it is a disease!
Know WHEN to dps. Do not use a heavy-hitter ability until the tank has proper control of the situation. If new adds come into the fray, STOP CASTING until the tanks have control once again - nothing is more frustrating to a tank than chasing errant mobs with taunts on cooldown.
Be aware of the encounters and mechanics, know how each boss fight works BEFORE you get in there. There are tons of wiki-style sites that detail instances and raid bosses, there's no excuse to not know how a fight plays out. It's like a role in a play, know your lines.
Be mobile and know WHEN to move. WoW is all about "not standing in it" when it comes to boss fights. Some battles are literally fought on the run and one misstep means you're dead. If something is glowing under your feet then GET OUT. If a firewall is rolling at you, follow the party to the gap. DO NOT FINISH YOUR CASTING. DO NOT KEYBOARD TURN. RUN LIKE HELL. You cannot DPS if you are dead.
Know when to pop mana regen items. Mages know to pop a mana gem early in the fight so later the cooldown is done, later they evocate later when the time is right. Shadow Priests unleash their Shadow Fiend on the boss early and later hit Dispersion, all the while they keep Vamp Touch alive to regen EVERYONE's mana. A potion is a last-ditch thing these days and cannot be relied upon. Endgame raiding is all about mana conservation and regen, even if you are a Warrior or Rogue... if you're healers can't heal you're dead.
Be patient. Expect to wipe, especially when the encounters are new. It will get tedious and expensive to repair, this is a given. Perhaps have a three-strike rule, if you don't get it in three attempts call it off until you can reconnoiter later with a better strategy or better gear.