Lets see...
For build, I still go oldschool and go with the Archangels+Rod core items, because I enjoy tankyness and the raw power that comes from that combination late game. I like Rod on her a lot, and you can build Morello or Athenes for CDR+mana regen if you prefer that route. She has a good deal of viable builds.
I run standard mage runes and masteries, and I max R>E>Q>W with one early point in W for utility. You always want E maxed, and against low dash compositions you can max W second if you want to teamfight early and think it appropriate.
There aren't really many tricks to playing her, but some of the little things include:
-You can cast your E on someone, then drop a single tick of your ult after it is in the air.
-Landing your Q is a bitch and a half, but if you can drop a W and your ult on someone you massively limit their dodge options and slow them down enough you should be able to double proc it most of the time.
-Use your very slow auto attack projectile to harass enemies under their tower, you can throw it and walk out of tower range before it connects.
-When taking jungle camps, you can wall them into their little pockets with W and kill them without taking much damage.
Anyways, what makes Anivia hard to play isn't her skills being super intense to micro the way that some other champions are. She just has really, really tough decision making. Her Q is a slow and long cooldown, but is an AoE stun and does a ton of damage. Her W can hurt your team as much as help it, but used right can make a team fight into a 2v5 or 3v5. Her R is a strong zoning skill, but also the most reliable way her Anivia to get the double-damage E so you want to find a way to position that you can use it for both.