The seed of druidism
The origins of druidism in World of Warcraft are not so clear if you are a stickler for details, particularly historical ones. The details seem outright odd to people from our cultural background, if you look at them closely. As it is written, the first master of druidic magic in WoW was the demigod Cenarius, who, strangely, was conceived through the mating of a mythical white stag god named Malorne and the probably humanoid goddess of the moon, Elune, who has never actually appeared to anyone in the flesh before and may not even have a physical form. Anyway, somehow Elune gave birth to this half-human, half-stag thing and then decided she couldn't bring him up on account of his being too "mortal" for her. Malorne decided he couldn't do such a good job either (possibly because he couldn't change a diaper with his antlers), and decided to give the baby to his other lover, the dragon Ysera. Why a dragon could raise a child (much less the child of his lover's other girlfriend), but neither a moon goddess nor a stag goddess could seems very odd -- but perhaps such a logical understanding isn't the point of the story in the first place.
Although Cenarius himself was a real, physical being in the Warcraft setting, the story of how he came to exist actually has a lot in common with many of the most ancient stories about gods and demigods in real human mythology. Children of weird mating relationships between humans and gods (or, yes, even animals) abound in such literature (don't even ask how the minotaur was born...), and yet they almost never seem to be intended as literal truth. Each one represents some aspect of the truth behind human nature and the relationship of human beings to the world around them.
Perhaps it is this sort of truth that Cenarius intended to convey when he shared the fanciful story of his creation with the night elves, rather than some sort of historical account. In a way, he was the father of night elf culture, as it was he that instilled into them their love of harmony with the natural world and gave them their ultimate sense of identity as the protectors of nature. In his story, he is born of a union of the earth and the sky, the practical stag god and the abstract moon goddess, and he represents the balance between apparent opposites in his teachings as well as his own physical form.
As the tree grows
Although the tauren also received Cenarius' teachings very early on in their history and continued to revere Cenarius long after the way of the druid had been forgotten, it was the night elves who really took hold of the druidic path and made it a central part of their civilization. Malfurion Stormrage was the first and greatest druid and for a long time he was a leader of his race, along with his lifemate, Tyrande Whisperwind. Together they represented the balance of male and female in their civilization, with most druids being men who followed in Malfurion's footsteps, and most priests being women who followed Tyrande. Malfurion and many of the other druids were required by Ysera, the dragon aspect of nature, to spend most of their lives in the Emerald Dream, watching over the balance of nature in the realm where natural energy itself comes from.
In times of great danger, the druids were awakened from this dream and charged with protecting the waking world of night elf society. In the Third War, many druids came back to the waking world, only to find that Cenarius had already been killed by the orcs early on in that conflict, when the orcs had once again been possessed by demonic bloodthirst. Although it must have been a crushing blow to many of them, they seem to have dealt with it in a spirit of adaptation and renewal rather than hate and vengeance. Even after the War against the burning legion, and the sacrifice of their World Tree, many druids have chosen to remain there to help confront the continuing threats to the world's safety. Those who have returned to the Emerald Dream, most notably Malfurion himself, have found that something is mysteriously amiss with the mystical realm of nature, and it is not so easy to return to the waking world.
In any case, since the events of the Third War, many tauren have once again taken up the druidic way, and have joined the night elves in the special organization of druids called the Cenarion Circle, which maintains the teachings and wisdom of Cenarius. Likewise, a number of women have started taking up the path of the druid, with some even rising to great prominence, such as Arch Druid Renferal. Even the path of druidism itself has gone through a number of changes -- whereas before the Third War, druids used to divide up according to which patron animal aspect they followed (with names such as Druids of the Talon, or Druids of the Claw), now many of them follow all the animal patrons at once as Druids of the Wild.
The fruits of natural thinking
Druids in the current setting are certainly dealing with a lot of change, but they don't seem to be very upset about it. In many ways, I expect change could come naturally to any people who make a systematic study of the natural world and integrate its lessons into their own life. They would undoubtedly learn that change is the very way of life, and adapt themselves to the needs of the moment. The druid talent trees are instructive of this sort of attitude: Balance and Restoration. Even spells like "Wrath," "Starfire," and "Cyclone" come under the category of Balance, indicating that, like nature itself, even a "Hurricane" of energy and destruction is, in the end, an essential stage of the cycle of life. Even the Feral aspect of druidic abilities reinforces the idea that, as with the great animal predators in nature, there must be a force of destruction that can keep the whole system healthy and thriving. At the same time, the natural system must undergo the special "Rebirth," "Rejuvenation," and "Regrowth" that can restore "Tranquility" and "Nourish" the new life that takes the place of the old. Your druid may identify with one of these aspects of the protection of nature more than the others, and view it as his or her particular specialty, or may view all three of them as an inseparable whole, whichever seems more attractive to you.
To get an even better idea of what it might be like to think as a druid, I would personally recommend going out and spending as much time in nature as you can. Even if you can't do that, however, it could help a lot to read some Taoist philosophy, and try to get a sense for the attitude of balance and harmony that Taoism tries to promote. You could also study a bit about nature-based religions such as Wicca, or even ethnic religions practiced by indigenous peoples around the world. Anyone who has studied a bit about the different ideas and attitudes of people whose goals and aims are so contrary to the modern culture of consumerism may have a lot to share with you as well; and there are more and more people investigating alternative worldviews all the time.
A summary of some of the more salient ideas from these philosophies is beyond the scope of this one article, but if there are many druid players out there who think it would be helpful, I may be able to share some preliminary reflections on their relationship to druidism later on. If you'd like more information about the real human druids of European history from whom the Warcraft characters get their names, we have a post here on WoW Insider from about a year ago about them and their connection to the druids of Azeroth.
All the World's a Stage continues this series on roleplaying within the lore with today's look at Druids. Be sure to check out Death Knights, Priests, Mages, Warlocks, Paladins, and Warriors (Horde and Alliance). For more about roleplaying the different classes, see how spells themselves can be used in roleplaying, for Druids, Hunters, and Mages, as well as Paladins, Priests, Shamans, Warlocks and Warriors.