It's a broad topic with plenty of broad answers; all of which are very key to making the most of being a balance druid. As a balance druid, as a raider in general, the best you can do is to know your strengths, know the encounter, know what is going on. In a game like World of Warcraft, knowledge really is power.
Tip 1: ABC
As Graylo mentions in his blog, always, always, always remember ABC - Always Be Casting. Always. No matter what you are doing, there is are very few situations where you could not be casting something, so cast! Reapply your DoTs - make sure Moonfire is second to help with having Nature's Grace up when you stop moving. If you have Typhoon, then I'd strongly suggest you grab yourself a Hunter alt to practice the jump-spin-cast-spin motion. Although it is much more difficult to pull off with Typhoon than Concussive or Arcane Shot, a balance druid can employ the same technique to effectively send a crashing wave of damage without missing a beat. If you've already done all that and you have 2 piece T10, then cast Gift of the Wild to get an Omen of Doom proc.
Knowing a boss encounter backwards and forwards is the key to any successful raider, especially to a balance druid. All raiders should have a mod similar to Deadly Boss Mods and if you don't have one, get one. More important than just getting it is using it. Many boss abilities fall on a very specific timer, all of which are tracked by things such as DBM by very handy bars. Watch them! Know what each bar means, know how it is going to effect you in the moments to come and adjust accordingly. If Insect Swarm just fell off, but you know that the boss is about to use an ability that is going to force you to move in 3 - 5 seconds, then wait to refresh the DoT.
Tip 3: Know the limit
Do not move unless you absolutely have to, and when you do move, do so as little as possible. Not only that, but time your movements. On an encounter like Lord Marrowgar, if you see a Coldflame heading towards you, then find the best time for you to move. Sometimes getting off that last cast is important, sometimes it isn't. If you are trying to proc Eclipse, then move sooner rather than later. If the Spores have just gone out on Festergut and you need to move to one but you have 3 seconds left on Eclipse, make use of that Eclipse time - you have time to get to that Spore.
Tip 4: Use everything
Know all of your tools, know how they work with each other, and use them in the most effective way possible. Waiting a few seconds to use Starfall after Lunar Eclipse ends to ensure Nature's Grace up time is better for your DPS than just using it the moment it comes off cool down. Also, if you know several additional targets are going to spawn in a few seconds, then wait for them to spawn before using Starfall. Tab over and throw some DoTs on a secondary target if you are forced into prolonged periods of movement. Properly time On Use trinkets to when they will be most effective - Spell Power/Crit for Solar Eclipse, Haste for Lunar Eclipse. If there are multiple adds that you need to AoE, try and coincide it with Starfall. If you can't, Typhoon the mobs before you begin to Hurricane to get Nature's Grace up.
Tip 5: Communicate
Talk with your guild mates and coordinate things. Raiding is a group effort, and everyone within the group should be communicating with each other to maximize their DPS. If you are going to be Power Infused by a Discipline Priest, then make a macro to let them know when you have Lunar Eclipse up to make the most of the effect. Going into every encounter, it should set out clearly for everyone when Bloodlust is going to be used this way you can properly time your Force of Nature and trinkets to get the maximum benefit. If, for some strange reason, you are getting Tricks of the Trade, then communicate with the Rogue to make the most of that effect. If you are capable of it, and likely at this point in gearing it is probably not as possible, then know and gear around have a Draenei in your party.
Beyond standard things such as that, communicate positioning and strategy with your guild. On an encounter such as Festergut, it would be silly to force a balance druid to stand out at range while having a Shadow Priest hunker down in melee. Stress the important of optimization of strategy to the guild.
If a lot of these tips seem like they are very general and could apply to virtually every class, that's because they are. Balance druids are not as far behind other classes as what people think; it's all about learning how to make the most out of every little thing that you do. For as simple as balance druids are within their rotation, they do have a relatively high skill cap, the skill, however, has less to do with being a good balance druid and more to do with being a good raider in general. Gemming, gearing, enchanting, and speccing properly are all important, but that is only a fraction of the real battle. Knowing how to be fully aware of what it going on around you, knowing how to make the most of each and every Eclipse proc, and not getting lost in all of the confusion really is what separates the 'good' balance druids from the 'great' balance druids.
Every week, Shifting Perspectives treks across Azeroth in pursuit of truth, beauty, and insight concerning the druid class. Sometimes it finds the latter, or something good enough for government work. Whether you're a Bear, Cat, Moonkin, Tree, or stuck in caster form, we've got the skinny on druid changes in patch 3.3, a look at the disappearance of the bear tank, and thoughts on why you should be playing the class (or why not).