For one, Arenas feel like a much more fair fight - whether 2v2, 3v3, or 5v5, the fight will be fairly balanced (ignoring all the 'overpowered!' QQ on the forums) and typically require much more skill and strategy. There is, of course, skill and strategy to be had in battlegrounds (particularly in pre-mades), but for the solitary person hopping into a random BG, especially if inexperienced, it can all seem chaotic and disjointed.
I'm still a die-hard PVEer at heart, so my current foray into the world of Arenas is mostly for fun and more importantly (for me, anyway) for knowledge and skills applicable to PVE. That's right - many things in PVP can greatly help your PVE skills!
I don't profess to be an expert in PVP or Arenas, but I'll touch on the spec and glyphs I'm using at the moment before moving on to some tips from Arena and their PVE relevance.
I have tried some 5s, but mostly I've been doing 2v2s with a DK in my guild. I've been playing with a 21/0/50 spec at the moment (though may try a slightly more offensive 21/0/50, taking Vengeance). The key point changes are in Natural Perfection and Improved Barkskin (for damage reduction) and Insect Swarm in the Balance tree (for more offensive utility). I've been picking up points in Celestial Focus in Balance for the spell haste (as I lose a lot of haste in my PVP gear) and the points in Brambles for the Dazed chance in an attempt to help slow opponents more. The glyphs I've been using have been Swiftmend (still a crucial glyph), Barkskin, and Insect Swarm (to increase its damage).
There are several things Arenas can teach you that can be very useful for PVE.
-Crowd Control (CC).
-Awareness (spatial and of teammates).
All of these can help you in ANY spec, I should add - not only while healing!
Also, while these suggestions are aimed at druids, they are an excellent jumping-off point to think about similar abilities in other classes as well.
Let's start with Defensive abilities.
When I first started healing, I'll admit, I rarely thought to use Barkskin and definitely didn't think to use Nature's Grasp. I actually only started even thinking about these spells after talking with a Tree friend a while back. We started discussing these abilities after a particularly epic (read: messy) Faction Champions fight which we were healing together and, after I ended up checking out the lovely woodwork on the floor of the Coliseum and he survived til the end of the fight, he started telling me about how he used these abilities in Arenas and how they helped him in the fight.
Using these abilities on Faction Champs is a pretty obvious correlation to Arenas, but both of these spells are useful in all PVE encounters. Barkskin, certainly, should always be on your bars. You can use it while stunned, frozen, incapacitated, feared, or asleep, in any of your forms. It is a straight damage reduction tool. If you miss a spore on Festergut, it will likely save your life on Pungent Blight, or if a stray add gets on you it will give you that extra second of survivability while the tank picks it up.
Nature's Grasp, particularly in its current inception (3 charges), is also excellent, especially on fights with adds or on trash. Whether you're in ICC or just running a 5-man dungeon, there may be a point where an add slips away from the tank or just decides you look tasty. Nature's Grasp can root it and give you that extra second again to get away.
Another great ability is Bear Form. Bear Form and Dire Bear Form, regardless of which spec you are, will increase your armour and your health. This is another great way to reduce incoming damage. Another key spell available in Bear Form is Frenzied Regeneration - this ability converts 10 rage per second into health for 10 seconds. If you're starved for rage, you can always pop Enrage as well; this will lower your armour (unless you have the T10 4-piece feral bonus) but help feed that heal. Whether you're an oom moonkin or tree needing a heal, needing the extra armour while healing yourself, or need a stronger heal than what you can muster as a feral, Frenzied Regen can be a great help.
For the DPS specs, this will likely be less of an issue for you, seeing as your primary role is offensive/damage dealing abilities.
Arenas can offer Trees some good practice at DPSing, though, and, more importantly, at balancing your offensive spells with healing. With most people outgearing heroics (and even outgearing some raids), it can be fairly easy and predictable to DPS while healing in PVE. The randomness of PVP in Arenas, though, can really sharpen your skills in recognizing when you can (and when you must) be offensive or defensive.
I picked up Insect Swarm in my 2v2 spec for this reason, to help increase the damage my teammate and I could place on opposing players and to provide another nuisance for them to deal with. I cannot, however, run in and mindlessly spam my Insect Swarm, Moonfire, or other spells. At the same time, though, if the healing required at the moment isn't as high, I shouldn't be sitting there doing nothing, I should be helping my partner. I need to be ready and able to switch what I'm doing and switch my targets quickly and strategically, whether I'm helping burn the last few hitpoints off one target, causing a nuisance to distract their healer off my partner's target, or making sure I don't fall behind on healing myself and my partner.
Also, in Resto, you will have to shift out of form to cast offensive spells. This will be changing in Cata (indeed, it's part of why Tree of Life form is changing, as the word from Ghostcrawler was they wanted to give us more offensive capabilities as Trees/make it so we were less penalized when using them (as shifting out of tree we lose our armour buff, our healing buff, and our spellpower buff). But it's something to keep in mind, and even more so now as we have to make conscious decisions about when we do shift to caster form.
A particularly key spell, both in Arenas but also in PVE (especially if you are the only druid in the group or raid), is Faerie Fire. It decreases a target's armour by 5% and, particularly key in Arenas, prevents the target from going stealth or invisible. This debuff can be of great help in PVE, particularly for physical damage classes.
-Crowd Control (CC).
Druids have several good forms of CC, the best of which being Cyclone.
Cyclone is an excellent CC, both in PVP and in PVE. In PVP perhaps you might use it to chain cyclone the opposing team's healer while you rip apart their dps partner (or vice versa), or alternating on dps targets while you wear each one down. The cycloned target becomes immune while stunned, so you can use it to prevent a target from receiving heals. It can also act as an interrupt of sorts - a well timed cyclone can stop a heal or cast going off.
In PVE, cyclone is an excellent way to CC mind-controlled players on certain fights (Lady Deathwhisper, for example) while also preventing them from being damaged by friendly-fire. (Some fights you cannot control MC'd people, however, such as on Blood Queen Lanathel). I also quite like it's cast-stopping effect and I find myself using that quite often, particularly in 5-mans (like in Old Kingdom when no one kills or interrupts the Spell Flinger's Shadowblast, which causes damage equal to 80% of the targets health). Cyclone can also be used in any spec - boomkins do not have to shift form to use it (trees and bears/cats do), trees can get an instant cast if they use Nature's Swiftness, ferals can get an instant cast when Predator's Swiftness procs.
Entangling Roots (along with Nature's Grasp) can root a target in place, giving people time to escape or simply holding the target in one place.
Bash in Bear will stun a target for 4 seconds and interrupt NPC spellcasting for 3 seconds. This is a nice back-up I find both in Arenas (particularly with casters) and in PVE with mind controlled people who have not been otherwise CC'd, particularly as the shift into Bear will grant you some additional armour. Feral Charge - Bear is also a useful interrupt for Feral druids to use against casters. Pounce is another fun stun, usable in any spec in cat form (though you must be stealthed), but it does apply a bleed, so not to be used against CC'd targets (particularly friendly targets!).
Hibernate is a particularly fun CC if you can get it off. This only works on beasts and dragonkin, but, druids (in bear, cat and travel form) and shamans in ghost wolf all count as beasts. This can be a handy way to deal with druids (especially feral ones), shamans if you can catch them in ghost wolf, and also hunter pets. I particularly like using this in BGs as with all the running, you're more likely to catch these players in forms (especially the shamans).
-Awareness (spatial and of teammates).
Awareness is key in anything and everything in WoW. Arenas can really sharpen your awareness as the encounter is much less predictable than a PVE encounter. You really need spatial awareness, awareness of your teammates and, building on that, awareness of other classes and their abilities.
Much like you don't want to stand in fire in a raid, you don't want to go toddling straight into incoming damage in an arena. A DK just threw out a DnD, you have to move out of it, you just saw the hunter fire a Freezing Arrow, you may want to avoid that direction for a couple of minutes to avoid getting frozen in an ice trap. You also need to be aware of the surroundings of the arena - are there obstacles that you could LoS your attackers with, or that your partner could get trapped behind and out of sight of you? Where is your partner, are they in range or not? If you're attacking one opponent, are you certain your partner isn't in the corner stun-locked by a rogue? If they are, what will you do about it? Have you been focussing so much on one player that you haven't noticed the other opponent is off in the corner preparing for another strike?
There's a lot going on that you need to pay attention to, and a lot you can do to act and react to the situations as they come. Use obstacles to your advantage - I (literally) spent 26 minutes kiting a shaman and a hunter around a big pole (much to their annoyance and my amusement), it took them forever to finish me off just because I kept slipping out of sight. Where can you see this in PVE? LoSing mystic buffet and frost bombs on Sindragosa, for one. Be aware of what's happening to your partner - they may need heals, or they may need you to put some pressure on the player that's wailing on them, or need your help in finishing off a target. Similarly in PVE, especially as a healer but also as any class or spec, being aware of the people you're raiding with and how you can help each other can greatly improve the raid.
Being aware of other classes and their abilities is also extremely helpful, both in PVP and PVE. In PVP, this might help you by knowing what abilities your partner has in his arsenal and by what you can expect from your opponents (and how to counter!). For example, Shamans will love to purge your buffs and HoTs off of you. Lifebloom, however, will Bloom if it is purged - healing you and returning mana in the process! Knowing this, you can use this to your advantage, using Lifebloom a lot and having the shaman either help you (by purging them off) or stop him purging altogether. You can also see when cooldowns are burned on targets (and know what cooldowns or abilities are available). For example, you put enough pressure on a Pally opponent that you forced him to Bubble. He'll now have the Forebearance debuff, where he'll be unable to use his other Bubbles or LoH on himself while that's up. That's also good to know in PVE - say your tank just had to pop Divine Protection (shield wall), he'll now have Forebearance and be unable to LoH himself. There are also dangerous CC abilities - while druids can shapeshift out of polymorph effects, a Warlock will be able to Banish a Tree (making you immune, but unable to act), another druid can cyclone or hibernate you, shadow priests can silence you... the list can go on!
There is a wealth of information about other classes and a whole host of abilities that can be helpful and harmful both in PVP and PVE, and as much as you can learn about them all, the better! If heading out and reading about them all seems a bit daunting, I highly recommend chatting with friends you have in other classes (I'm sure they'd love to chat about what they do! I always have fun on both sides of conversations like that, whether learning about someone else's class or telling them about my own), or checking it out for yourself and playing with the abilities by playing an alt.
Mobility is pretty key for druids in all specs and we have a range of abilities that make us all the more mobile. We can shapeshift out of polymorphs and snares (incidentally, a great macro for PVE and PVP is '/use !___ Form', ie, /use !Tree Form. Using this will shift you right back into that form (ie /use !Cat Form, or /use !Dire Bear Form) in one GCD without stopping into caster form, which can be key for retaining armour or utility at certain times).
We can shift into Cat form and Dash to sprint away, we can shift into Travel Form for 60% increased movement speed. We can cast HoTs on the go. We can do a Nature's Grasp, Cyclone, or Roots and Dash away, we can even go into Aquatic form and swim away! We have many instant spells (both damage-dealing and healing), feral charge -bear and -cat in feral. On and on! Yes, there are times when we need to stop and cast, but we are for the most part free to move, so there's no reason why a druid should ever be stood dead still in someplace they shouldn't be! Or else you'll end up, well, dead.
Well, that is all for now! I hope you have found this useful and perhaps may look to venture into the world of arenas as well. I'll see about posting more on arenas in future as I get some more experience, for some good information now though specific to arenas, I recommend some of these links:
WoW PvP Forums; WoW Druid Forum - PvP Feral Guide; WoW Druid Forum - PvP Resto Guide; Arena Junkies.