Note, this is not a guide to build an Annie that will burn down one or two enemies by blowing all her cooldowns. The point of this Annie build is a fantastic TEAM character, with a strong burst combined with the ability to contribute steady, sustained damage in a fight, while giving enough survivability so you don't get destroyed instantly in a team fight, and allowing you to pick your spot and AoE stun at the right time. Also, this build maxes out cooldown reduction, which, with correct spell chaining, will let you get your stun up every 5 seconds. Lastly, if you are just starting out with Annie, don't be afraid to hop in a side lane and let a team mate help you out. Otherwise, grab that mid, and dominate anyone who dares enter.

Ok, so these runes are completely re-workable based upon your preference and what runes you may have available at this time. For the yellow seals, I prefer flat Mp5 because I'll be buying more Mp5 later with Morello's Evil Tome. However, Mp5 per level runes are just as good. Secondly, flat cooldown reduction runes are also an option instead of CDR per 5, however I'm cheap and didn't want to fork out the extra IP for what I would consider a negligible boost in your early game. Again, it's up to you. Lastly, I cannot stress enough how important Magic Pen is. In my experience, the enemy team invariably ends up building Banshee's Veils across the board, and the 72 Magic Pen that you'll have by end game will let you chew through casters MR items and deal some nice damage to any tanks that try and get in your face.

Here again, masteries are a preference-based build. However, there are some core masteries that must be picked. You have to build 9/0/21. There is no other way to build Annie's masteries and still maximize her potential. I like Good Hands over Preservation because, as an AP Carry, you will get focused, and you will die. This just brings you back faster, but it's totally up to you. Next, Awareness is just such a clutch mastery, and mana really isn't a concern after you buy your first mana crystal. I don't pick Greed because Annie farms extremely well, collects lots of kills, and the extra gold won't help. Utility Mastery is actually really useful with Annie, especially if you pick up a blue buff before you've build Morello's. The last masteries are self-explanatory, but feel free to take a point out of Blink of an Eye or Utility Mastery and put it in Greed if you so choose.

I start with Doran's Ring because, well, it's really the best starting item for Annie. AP, Mp5, and Health? Sign me up. Depending on how well you are doing in your lane, you can rush Sorcerer's Boots. However, I usually end up going back (after First Blood, of course) with around 800 gold and grab level 1 boots, a mana crystal, and a couple of health pots. After that, the item progression is pretty standard. Rush RoA, then grab that Rabadon's and start melting faces. I prefer to buy an Elixir of Brilliance right after Rabadon's to, one, max the bonus AP you receive from the elixir, due to Rabadon's Unique Passive, and second, to grab that 10 percent CDR before you've started working on Morello's. The Void Staff is purely a late game item, and depending on the enemy team, you may want to build Banshee's Veil first. Either way, sell Doran's Ring once you want to start building your last item. I've played around with Rylai's Crystal Scepter, and it's passive ability, combined with health and AP, is really nice, however the Banshee's Veil will for sure keep you alive longer. Also, not a big fan of snowballing with Mejai's. This item build at end game, combined with your Molten Shield ability, will allow you to take a beating without getting melted and still put out substantial damage.

I start with Q because it is Annie's best friend when it comes to farming. Last hit like a champion with Q to build up your stun counts and keep your mana pool filled up. I know many builds have Annie max Q first, however Annie's W has a higher base damage count. I max W for the sole purpose of killing the enemy champion in your lane. The absolute destruction that Annie's W does at skill level 3 (You'll be at Level 5 at this point in time) will put the fear of God in the enemy champion. This also takes a bit of playing possum. You should be last hitting minions with Q until level 5. Once you reach that level, get Annie's passive stun ready, tag the enemy with a Q, then melt with W. Half their health should be gone, and as soon as you reach level 6, get that stun up, and either catch the enemy with your ult, or push the envelope and Flash in, Ult, Q, W, Ignite, and they will be dead. Rinse and repeat. I can't stress enough how godlike the burst is from Annie's W, so max it out, and burn'em up.
Lastly, Flash and Ignite are pretty much necessities for Annie. You can replace Ignite with Ghost if you're having trouble surviving or just learning how to use her, but otherwise, those are the only two summoner spells you should have.

So to conclude this over long explanation of Annie, the main point of this Annie build is STUN PLACEMENT and TIMING. You are going to do damage. Whether you build a 700 AP glass cannon or a 400 AP survivor, Annie will do lots of damage. This build will keep you alive, and if teams decide to get out of position just to focus you down, they will pay for that mistake dearly when they realize that you're not dead after five seconds, and they're own squishies are getting crushed. Most importantly, the reason for staying alive is for that delicious stun. With increased survivability, you don't have to rush in there and try to grab as many people in your AoE stun as you can, blow all your abilities, then get crushed by the people you didn't stun. Instead, you can pick your spot and wait for the right time to Ult. That being said, throw your other abilities while you are waiting. Stun single champions out of they're ults with Q, or maybe the other team's beefy chars are charging forward, then throw you W on them to stun them both, then spam your abilities over the next 5-7 seconds to get the stun back up on your Ultimate. Annie's Ult should be used to nuke squishies, capture multiple enemies out of position, initiate (if need be, but definitely not my favorite use) and generally wreak havoc and turn a team fight in your team's favor every time.
Thanks for reading, I hope this helps!