In general, Annie is known for her stun, high burst, and her cuteness lol.
Playing Annie in game has two main purpose:
1. To burst down the AP or AD carry quickly.
2. To provide area stun.

While the initial high burst damage of the RQWQ combo is substantial, Annie's strength is greatly reduced if the oppoenents has some MR or health that you cannot burst him down. At the same time, you may sometimes spot that tank like Shyvana or Jarven can dominate the battle. So here, the article would utilize the huge potential base damage of Annie, which is always overlooked -- the Tibbers.

That does not make any difference from the AP Annie. They focus on early level laning and advantage. So I would not comment much on that.

Here comes the main difference!
You are pursuing DC, Void Staff and your opponents are looking for MR and health.
If you burst the carry down, you win. If you cannot, probably they win.
This is quite a problem when you are playing AP Annie, who is a mid range mage.
Despite the high AP ratio, Annie also has high base damage with Tibbers. This gives her room for some builds of survivability.

The main build is ROA, for lane sustain; then Rylai, for more health.
At this point, you may not get many kills, but you definitely would not die that much!

Your damage would solidify after the tourment. I would explain in the following. Finally, an hourglass help you to bait opponents and survive critical moments.

The remaining just depends on situation. But! Focus on survive and defend, NO DC or AP stuff. The increase in AP do not contribute much in this build.

Early game

Normal play from lv1-8. You still have your advantage of high burst. An all-in combo may still kill the opponent mid.

Mid game

As you do not get DC later on, your damage may lag behind. But you have great survivabilty. Now your main damage output is from the Tibbers. Try to stay away from the opponent while leaving the Tibbers with them. Sometimes they may chase you, just kite them with QW and the Tibbers would do damage to them.

Late game

Here comes the mask, the DPS could be substantial with Tibbers. Sometimes you can just stand there and play a 2v1 - Opponent vs you and Tibber. You could always survive with the increased health. With the hourglass you could bait opponent to chase you then activate the item, Tibbers would help you finish them.

So try and have fun. :) Let me know if there is any problem.
This is my first guide and I just want to share some fun builds:)