Roots + Moonfire: Just root them, then moon them, let it do it's DoT, then repeat. Very slow, but helps against mobs one or two levels higher than you. Almost a certain win, just gotta be quick with the roots.
Soften Target: For equal level mobs or less, root, moon, then wrath or star until roots break. As they close in on you, cast rejuv on yourself, shift to Bear, finish them with melee, using Demorale Roar and Maul. You'll regen MP as you do this.
After that, if you have enough HP to take another mob, use the rage enhancing ability, wait for it to finish, then attack the next mob. If you don't have enough HP, swap to caster, heal up, start over.
Healing a shifter: If you're meleeing in bear or cat, once you hit around 1/2 to 1/3 life (depending on # of mobs, mob lvls, etc), shift back to caster. If tauren, use stun to buy you time. Then use Regrowth (fast cast) on yourself, then cast Rejuv (insta cast). Shift back to Bear or Cat, finish them off. This works well against mobs higher level than you, but you gotta be quick.
Against runners: I hate these. Either just use roots and wrath, or prepare to shift back to caster when the mob gets low on hp. Then use spam moonfire (instant cast) as he runs away, although this is hard on the mp. You can try to stun him as Bear when he gets low, but if you miss...
Against stuff lower level: If only one, use cat, and spam Claw. Faster than Bear or Caster. Use your finisher against runners when they hit 1/3 life. Switch to Caster to heal when needed.
But if they are close to your level, be prepared to shift to caster to heal yourself mid-fight.
If you get an add, shift to caster, heal, then go to Bear. Cat cannot take much punishment.
If facing multiples, weaken one w/ moonfire, rejuv yourself, then go Bear.
Meleeing as caster: Wack them with your staff, casting rejuv on yourself, and moonfire on the mob (all insta casts). If you get low on hp, cast regrowth (fast cast, Healing touch is more of a group spell). If getting low on mp, switch to Bear (gives you more time to regen mp than Cat).
Crowd Control: If you get a beast or lizard add, use Hibernate on the party pooper. Then resume beating on your original target, you got 20 seconds. Just make sure to select the mob that is NOT asleep, or you'll just wake him up. Also, poison, moonfire's DoT, or roots will wake him up as well.
Running: If against a beast, Hibernate him once moonfire wears off. Against anything else, root then run. Or if you put a point into Nature's Grasp (recommended), cast that as you run away.
Indoors? Bring Swiftness Potions.
Also, consider shifting to Cat and Dashing away, if you have the mp.