Overview
While there are many details to how to run fast raids, they boil down to three general principles.
This guide is a condensed version of PULL! A Guide to Faster Raids
Guide
Minimize Trash
Both minimize the amount of trash you pull, and the time you spend on trash.
While at the start you may want to pull every pack to increaes your chances of getting BoP epic drops, there's no reason to continue to kill every mob in the instance after you have what you need.
Most raiders are in the habit of tuning out that stuff in between bosses that is called "trash". It's a popular time to take extended AFK's, both announced and unannounced, and to just play poorly in general. "Trash doesn't matter" is what one mage told me a couple of years ago.
Unfortunately the longer you spend on trash, the less you get done that night -- and a big percentage of that time will have been spent on trash.
The biggest tip for clearing trash quickly is having an impatient puller: as long as they responsibly pull (using an add-on to see health/mana status), having mobs in camp almost constantly will dramatically speed up your clear times.
Minimize Downtime
One of the biggest contributors to raid downtime is loot. Regardless of what system you use, it's probably taking up too much time. Time yourself next time: even if you take only five minutes per boss to do loot, that's 75 minutes of loot distribution for the fifteen Naxx bosses.
Ideally, use master looter, so at least you can start clearing trash while loot is handled.
Plan AFK breaks: one at the start, and one mid-raid. This will reduce the amount of random AFK's because people will know when they can step away.
Don't ask questions that the entire raid has to answer: "Everyone ready?" will take a long time to get answers. Ask: "Who isn't ready?" Or better yet, don't ask -- tell the raid "Pulling in 15 seconds" and let people speak up if they have an issue.
Lead Effectively
Don't let fears of wiping stop you from pushing your raid: there's nothing wrong with a few wipes, and that's the best way to learn what your current limits are.
Make sure you keep the communication lines open: your tanks and healers need to be comfortable with each other if you want to pick up the pace.
Don't get so tense that your raids stop being fun: you don't need to be a dictator in order to run efficient raids, and there's still lots of room for joking and relaxing on vent.
Train your raiders to set up for the boss before you reach him and then do a fast review of the highlights right before engage. Don't feel bad if your raid performs best when you call out things like waves on Sarth or reminding them to get people off the walls on Maexxna: that's normal, all guilds are that way, and it's better to say a few words on vent than wipe due to a brainfart.
The most important thing you can do as a raidleader is delegate: don't handle everything yourself. The buck stops with you, but that doesn't mean you should do all the work.
