Here is a quick tips list for how to up your DPS when you first start raiding. You will quickly find that raiding is not like 5mans, and 10mans are much less forgiving than 25 mans. So here are some ideas on where you can start looking so that you can be the best you can be as a DPSer.
Be raid aware - You cant DPS dead. I often find that this is the easiest and best way to improve raid DPS. Learn the fights, watch movies on youtube, read up on bosses. Get DBM or bigwigs installed so you know when boss CDs come up or when they are going to use an ability. Time your trinkets and other CDs for the right time. Call out heroisms so people all pop trinkets and CDs (for example treants + heroism is win for aboomkin) together with a heroism. Get co-ordinated and work as a well oiled team :)
Know your class - go read up on what all the cool kids are doing these days with spells and rotations and stuff.EJ is a good place if you like numbers and spreadsheets, MMO champion is also a decent place to start. And if all that is too much, try wowwiki.
Know your gear - What you have and what you need and where to get it. Get Rawr, use the Armory, look at atlasloot ingame. Make a plan, what you need, where it drops and enact that plan.
Know your gems/enchants/glyphs etc - go get a socket for your belt, give someone an enchanting point and get your gear enchanted. Learn which glyphs you should be using for your spec and rotation. No seriously, do it. Do it NOW and as soon as you get new gear. Bring mats with you to raids so you can instantly use new gear.
Know your stats - hit is the single most important stat if you think your DPS is low. Melee/huntards do much of their DPS from white damage, the more your miss the more your DPS will drop. locks and mages need hit to actually have their spells LAND. There are plenty of things out there on the net to help you. Learn the way of Google Fu.
Learn the difference between crit and haste and how much you should have of each (it is a very difficult concept to know the difference between throughput and DPS, but they ARE different) they are stats which should be balanced - find your sweet spot for your class and spec.
Know your threat and your tank - By this I mean their TPS. Learn what your tanks average TPS is, and how hard and fast you can cast and still maintain a safe buffer on the threat meters for those crits. Know where you can sit safely and pump out the most DPS based on what your tank is capable of. If you are having issues, perhaps talk to your tank about what they can do to help up their TPS as well as looking at what you can do to reduce threat.
GET MODS - first up get quartz. this will improve your throughput by letting you know what your current lag is. Cast the next spell in your rotation as soon as your cast bar hits the red. EVERY caster should have this or a similar mod (yes even healers).
Next get Omen. This is a totally essential mod, learn how it works, learn what all the options mean and where you should be aiming for on the meters relative to your tank.
Get DBM or bigwigs (see above)
Get Ora2 or CTRA so you can set your tank lists and all kinds of other nifty raid features the more people in the raid have them, the more useful they are as a tool.
Get raidframes of some kind - they provide so much more information than the vanilla frames it is stupid and blizzard are looking into fixing it.
Get recount, now this will give you a immediate feedback on what of your spells is doing the most damage so you can maximise output. THIS IS NOT FOR A PISSING CONTEST! It will also show you real time what the raid DPS is (really handy) and how fiddling with it affects your real output.
There are more mods than this, but these are the basics I would recommend.
Know your consumables - you can cover off gaps in your character with food buffs and pots and flasks and elixirs. There is +40 hit food available, MP5, SD, Haste, expertise... all kinds of things. You should all have consumables up all the time. If you don't you are letting your raidmates down. DRINK POWERTHIRST!