So you don't have to follow my build/guide 100%, but the magic pen build will help.

AS FOR ABILITIES, THIS IS WHERE I HELP YOU!

So, for build, get sorcerer's shoes/haunting guise/void staff/abyssal scepter for the EPIC MAGIC PEN and of course rabadons/zhonyas/deathfires for the AP. Blahblahblah. YOU DO NEED, HOWEVER, MANA REGEN! Doran's rings are very good if you can farm; if you like poking get that spellthief thing. If you dont like farming/cant farm much get that ancient coin; it will help you in the long run, so only sell it like late mid game or early late game. Or even late-late game!

As for abilities, this is actually where I help you. Yes I repeated myself.
Stack your passive (THE STUNS MAN) at 3 charges (at 4 when it lights up orange they can see the swirly twirly stoof around you) and when you need to go balls deep or defend urself, I reccommend using ur ult as stun because TIBBERS HAS HELLA AOE WHEN HE GETS CAST! So, e before r, and bam! Giant AOE stun and dmg! Then smack with w, use ur q on the most annoying enemy opponent, and you're pretty much set. If you're on cooldown by then, run the **** away. Just run. Dont even think about it. Esp. if you're low, dont even do ur combo afterward unless they're on the way or you dont move towards them. JUST RUN. Anyways, yeah, that's that.

For 1v1 instead of teamfight AOEness, still use tibbers for stun, but your q is a better stun tactic as it is a guaranteed hit once it casts, right? Then chase, follow up with w or r if you have it off cooldown (I STILL RECCOMMEND R AS STUN AS U CAN USE Q AS CONFIRMED KILL AND SPEND THE TIME IT FLIES TO UR TARGET TO RUN THE F**K AWAY) but honestly once annie stuns, she just can do hella dmg. So I reccommend rushing magic pen because they will rush mr to counter you, so you counter their counter and win. DONE! Then you're fed, they're not (or they're LESS fed), and you get your AP to amplify your magic pen. Plus, void staff and abyssal give you AP WITH the pen and abyssal also gives you MR! Yay! Liandry's I don't really like, but it gives you magic pen as well as DOT if they have full health (so the initial tibbersness stun) and a good chunk of health. ROA (rod of ages) gives you health, ap, and mana. Good stuff.

Annie is a 450IP champ but if you build her and play her right she is VERY broken. Annie support is pretty much rush mana regen and gold regen and then later get the magic pens and let your ADC take the kills. Then you can get fed later. Simple.

Remember the COOP vs AI times, but Intermediate bots? Annie bot? Udyr bot? Well, let me tell you that Udyr bot turret dives hella for no reason like shyvana bot in intermediate, and what does Annie bot build? FLAT F**KIN MAGIC PEN. Is it fair? NO ITS F**KIN BROKEN. She ults to stun, w to stun and lands it perfectly, q to stun for trolls, pretty much you get screwed either way. So, follow that example.