DRUID LEVELING: LET'S GET THIS SHOW ON THE MOSS-COVERED ROAD
Welcome to your shiny new Druid, and a secondary welcome to the hell of caster form gameplay. If all goes well for you, you will be seeing this form as little as possible for the REST OF YOUR LIFE. One more note before we start -- I assume here that you do not have access to BoA items and that this is a brand-new Druid on a realm where you have no toons (i.e., worst-case scenario for leveling). If your wee Druid has a few more advantages than that, then leveling will simply go by more quickly for you and you can disregard some of my upcoming warnings concerning the difficulty of certain mobs.
The Druid begins with the following abilities:
1. Basic melee.
Nothing to write home about, but you'll be using it more than you'd think.
2. Healing Touch.
In later levels this will be a time-consuming "big heal," but for the moment it's relatively efficient.
If you go Balance, you'll be using a lot of this all the way through 80. For now, this is your main nuke, and it's quick to cast with medium-ish damage.
4. Either Shadowmeld (as a Night Elf) or War Stomp (as a Tauren).
Both are excellent emergency abilities, and ones that I advise you to get used to using both quickly and preemptively. A War Stomp + heal or War Stomp + fleeing combination for a Tauren is a lifesaver; running yourself to a safer area then Shadowmelding for a Night Elf accomplishes the same task (if your character's low on mana, try not to Shadowmeld in an area likely to be repopulated by hostile NPC's soon).
DPS at this level is fairly straightforward; start as far away from mobs as you can and cast Wrath until you go OOM or close to it. Whatever's still alive when it reaches you is just going to have to be beaten into submission. Low-level mobs typically die within the space of 3-5 Wraths, but you'll be forced into melee fairly quickly if you're chain-pulling. Use that as time to regenerate mana, heal up, and keep going.
Yes, caster form's melee DPS is a sick joke, but hang in there.
Here you'll get your first rank of Mark of the Wild, which at this level is a fairly uninspiring +25 armor but eventually develops into a great, all-purpose buff. Get used to keeping it up at all times.
Your two new abilities here are the much-fabled Moonfire and the first rank of Rejuvenation. Both are core abilities that you will be using a great deal all the way through to 80 (indeed, Rejuvenation still accounts for the largest percentage of +healing done by Restoration Druids in today's raids).
Moonfire is a bit of a mana-guzzler, but is still a mana-efficient DoT if it's allowed to run its full course. Rejuvenation is actually slightly less mana efficient than Healing Touch at this stage, but is the better heal to use if your character isn't too badly damaged but could use a heal before pulling the next mob.
With Moonfire now in your arsenal, you have the choice of pulling with that spell then spamming Wrath on mobs, although you'll probably expose yourself to a little extra damage that way, and here's why; Wrath's travel time allows you to be in the middle of casting another spell by the time the first Wrath hits the mob you want, whereas Moonfire is instant and you'll be on the GCD as soon as you aggro a mob. Due to this, in general I find it slightly faster to continue DPSing mobs down with a mixture of Wrath spam and melee, but experiment and see what works for you.
Thorns is your new spell here in addition to a second rank of Wrath. As with Mark of the Wild, get used to keeping Thorns on yourself at all times, although this is a bit more of a nuisance as Thorns is such a short-duration (10 minutes) spell. Fortunately, you can use a minor glyph (Glyph of Thorns) later to make this less of a nuisance, but for now, just keep an eye on your buffs. Thorns doesn't add a lot of DPS, but it will improve the rate at which something dies once it's beating on you (and if you go on to tank later, be especially vigilant about making sure it never falls off).
Your second rank of Healing Touch arrives, and you'll get a new and enormously useful spell here (particularly if you're leveling Balance): Entangling Roots. Roots is the Druid's only crowd-control spell until Cyclone at 70 (unless you count a Feral stun, I suppose), and it -- for lack of a more descriptive term -- literally roots a hostile mob or player in place. The NPC/player in question retains all of their abilities but simply can't move, so a ranged mob is still going to keep shooting at you if rooted. Keep that in mind if you're using Roots as an escape mechanism while you're low on health.
While Wrath spam is still the fastest way to DPS a mob down at this stage (and Entangling Roots breaks to damage rather quickly, unless you decide to glyph it later), you can avoid a lot of damage by casting Wrath at a mob, Rooting it immediately after Wrath hits, then continuing to DPS. However, if you're low on mana, Moonfire + Roots is a surprisingly potent combination on low-level mobs.