Perhaps the most difficult kind of druid to engage in PvP is the restoration druid. This isn't because they are powerful enough to kill you -- they likely aren't -- but because restoration druids are almost never alone. This changes the dynamic of a PvP encounter in that restoration is a support spec and is intended to give the most advantage to friends who do have the power to kill you. It becomes difficult, then, to give specific pointers as to how to deal with a healer druid because most of the time your attention will be divided between the druid and her partner.
It is extremely difficult to outdamage the heals of a restoration druid. They can and will stack HoTs and pull off well-timed Swiftmends that pump up their targets (possibly themselves) to full health. The basic idea against druid healing is to keep removing them, forcing the druid to resort to direct heals such as Healing Touch, which isn't the most mana-efficient or fastest-casting spell in her arsenal. It's extremely bad to allow a druid to pull off a Nourish on a target with full HoTs. Removing HoTs as soon as they are applied also eats up into a restoration druid's considerable mana pool, and this is key to the fight because a druid with a lot of mana can pretty much keep anyone up indefinitely.
In the battlegrounds, it's extremely important to call attention to the healer, particularly a restoration druid who can apply Rejuvenation liberally on her allies. It will take much coordination, too, since druids as mentioned have a plethora of abilities at their disposal to facilitate escape. For the most part, a restoration druid can pretty much survive simply by keeping HoTs on herself and throwing the occasional Innervate to recoup mana. It takes an inordinate amount of DPS to take down a druid concentrating on survival.
By the same token, an unfettered druid can keep her partners alive. Thus, crowd controls and interrupts should be applied judiciously to the druid. For example, if you are able to remove all HoTs, take the druid out of play with a well-timed crowd control spell (probably a taste of their own medicine such as a Cyclone) and focus fire on the DPS. Conversely, even the best or most well-geared healers will have trouble staying alive through intense focus fire. Again, it's difficult to predict these things because the dynamic changes greatly against a restoration druid.
Druids wary of buff removal can also use Wild Growth, which dispenses a greater part of its healing in the beginning and tapering off in the end. Clever druids won't shift into Tree of Life form until engagement begins in order not to attract attention upon themselves. It is extremely difficult to stop druids from casting heals because they just have so many instant cast spells at their disposal. The trick here then is mostly damage control -- or more specifically, heal control. Don't allow HoTs to get out of hand. Restoration druids won't hesitate to toss a Rejuvenation on a target with full health as the HoT provides a measure of mitigation.
In the best case scenario, a druid can be interrupted while casting a long-cast heal such as Healing Touch or even Cyclone. What you're going for here is a school lockout, which prevents the druid from accessing any Nature spells. In some cases, this should provide a good enough opening to deal significant and hopefully irrecoverable damage to the druid or her companion(s). It's unlikely, but whenever you're up against a healer, you hope for the best.
The most dangerous thing about restoration druids is that they aren't limited to heals. Remember that they can still shift into bear form and stun or interrupt opposing spellcasters or healers. They can shift into travel form and create distance. They have access to Entangling Roots, too, and the best druids are experts at using Cyclone to take opponents out of play. Because their focus is on survival -- whether their own or their allies' -- restoration druids are more likely to use their various abilities to keep enemies at bay. Your best chance at an interrupt, in fact, is when they pause to use these crowd control abilities and snares.
Ultimately, fighting a restoration druid is all about keeping them under control. They will very rarely be caught in their humanoid form because their arsenal of heals is accessible to them in tree form, anyway. It is important to watch out for their buffs, as most of it is key to their success. Unless there's a massive disparity in your damage output and your target Restoration druid's healing capability, you're better off moving on to another target as it's highly unlikely you'll be taking them down. My best advice? If you see one, just do a /dance emote. Who knows, she might oblige. Ever seen a tree do the twist?