This is how I build Annie in mostly solo-que games. This is my first guide so please try and be constructive not destructive with your comments.

I love Annie for her sheer nuking ability, a fed Annie is very scary.
But she also tends to be the number one on your enemies hit list.

For runes I take basic AP caster runes.

Magic Penetration Marks
MP5 per level Seals
AP per level Glyphs
and flat AP Quintessences

The reason I take MP5 per level over AP is so when you harass with your Disintegrate you can regenerate the mana back faster. It is also useful if you lane with someone like Gangplank, when you both compete for last hits on minions and you don't get the mana back because Gangplanks Parley got the kill instead of your Disintegrate.

Again I took standard AP caster masteries 9/0/21 going for mana, mana regeneration, movement speed, and ability cool downs.

I don't take greed in the utility tree because most games last between 30 to 40 mins.
1 gold per 10 seconds means 6 gold per minute which means 180 gold after 30 minutes and 240 for a 40 minute game. And in the rare case of a game that lasts an entire hour it would give you 360 gold. You start the game with more gold than that so I find Greed to be fairly useless.

I also don't take Utility Mastery for the simple fact that I rarely go for blue or red buff in games.

I start of with Doran's Ring for obvious reasons. The HP is the biggest reason I get it, early game Annie is very squishy and this helps reduce her squishyness. So why not get a Ruby Crystal if all I am going for is the HP? Because with Doran's Ring and you flat AP quints, you can hit pretty hard at level one. I also grab a HP pot for when the enemy team harasses me past half HP.
I then rush Majai's within reason in my opinion. I grab a Catalyst The Protector for the HP and mana, also its nice to have the level up bonus. I grab basic boots for the speed increase to get around faster and chase runners. After i have what I believe is the necessary survival items I grab a Majai's and start killing as much as I can. Then I finish my boots, which can be any depending on the enemy team, but i like to get sorc shoes for the magic pen. I then grab a Rod of Ages for survivability and AP. Then I go for straight AP items starting with Rabadon's Deathcap, Void Staff or Abyssal Scepter depending on the enemy's MR, and top it off with a Zhonyah's Hourglass.
But remember items are always subject to change depending on the enemy's team make up. If they are heavy on stuns you might want to turn you catalyst into a Banshee's Veil instead of a Rod of Ages. Same goes for your shoe choice, heavy melee team go for Ninja Tabi, heavy CC team Merc Treads, etc.

I get Disintegrate first so I can start farming minions right off the bat, followed by Incinerate. I try and keep those two abilities around the same level so when I harass my Disintegrate doesn't do all the damage then my Incinerate does mediocre damage. At level 5 I grab Molten Shield for two reasons: One for the bonus defense and the damage return and Two to help me build up my stun for when I hit six and start the murdering with Tibbers.

I like to get Flash and Ignite for its ganking ability. Flash in, with stun ready, Tibbers Incinerate Disintegrate and if they aren't dead Ignite.

You can also choose Ghost over Flash, but personally I like Flash.

Early Game

In early game your main goal is to get last hits on minions with your Disintegrate ability.
Do not think you are wasting your passive on minions, it will charge up again and again.
Now if the enemy hero is dumb enough to get in range while you have your stun up by all means throw the Disintegrate Incinerate combo on 'em.

Mid Game

After you get your Majai's you want to focus on getting kills, gank all lanes if you can Annie can be a great ganker with her giant Tibbers stun. But always keep in mind that after you throw all you have at them you are vulnerable for a few seconds until your spells are off cooldown, so try and make sure your target is low enough to die or get very low after your nuke.

Late Game

At this point you are either doing amazing damage or average damage, depending on your items and the amount of stack your Majai's has. Annie should typically be hiding in a bush till a fight breaks out then you go in AoE stun with Tibbers and Incinerate the one that got stunned then pick off the lowest HP enemy with Disintegrate. And make sure you have Molten Shield up before you charge in for the bonus defense in case the enemy team give you the death eye. But in some cases Her AoE Tibbers stun can be a good initiator, stunning all those in reach and doing good damage could inspire you teammates to charge in.

All in all Annie is a standard AP caster nuke, while my guide most likely will not open your mind to new ways to play her I hope it will give you the basic understanding of how to play this under loved champion.