Simply watch this video if you do not want to read, it uses Aion as a reference but the same mechanics apply to all classes in LOTRO.
Now, basically what most people do when ever they are fighting is simply use their skills. Doing this provides you with only a fraction of the possible damage you can actually output alone. I have tested this technique on champions and hunters with success, but have not tested any other classes, that being said I am positive it will work on all characters for most skills, if not all of them.
Basically the technique involves weaving, or adding in auto attacks between skills, but timing it perfectly to the point where you cancel your auto attack animation completely. When done on a champion you simply wait for your weapon to move from its starting position, then use a skill, and repeat. Alternatively you can simply wait for your auto attack and then use a skill, but this does not increase your DPS by much the longer the time you add between auto attacks and skills.
As a hunter right clicking a mob to attack it and then using a skill immediately after will start your chains of auto attacks and skills. When successfully done you will begin your induction time for your skill, for example quick shot, but at the same time you will see your arrow get shot. This means you can get an auto attack off and start your induction time at nearly the exact same time, saving you time for every skill used, as well as increasing your DPS.
I have yet to see any one do this when killing anything so I think people simply do not know about attack animation canceling. I hope this helps some of you increase your current DPS, and I am sure some of you will be surprised how much more dmg you are doing simply by adding an auto attack between every single skill cast. One major pro from doing this, besides the increased DPS, is the longer lasting amount of power you have, especially if you are a champion who notices your power depleted in a short duration.
For a champion I found 2H wep + using this technique to provide far better DPS than 2 single handed weapons, even though there are more skills that provide off hand damage. Walking up to a mob and using an auto attack and a skill at the same time resulting in a mobs instant death is to good to pass up, certainly not possible for me to do with two low dmg one handed weps which provide lower crit dmg.