This is a simple build that I use quite regularly to lane Annie. Many think because she's ranged that she should automatically play the middle lane, but quite often there is a much better suited Champion because Annie has low health early game. Thus when another teammate requests mid with their champion, pull this build out, and surprise the enemy team with Annie on the either the top or bottom lanes.

The items are pretty straight forward, I think. They are all found under Ability Power save the shoes (Movement) and the Thornmail (Armor). One thing to note here is that while the Thornmail is not typical of any build for a mage such as Annie, it can prove quite useful later game if you find your self taking a lot of hits. If the other team is not focusing you, then you can switch it for another Rabadon's Deathcap for the extra Ability Power which is very recommended. The Void Staff and the Archangel's Staff order can be reversed if you find yourself running out of mana too quickly early game. Also you can purchase consumables to boost your mana, but they are only temporary. The idea behind these items is that the summoner already has the skill to make up for their deficiencies and maximize their strengths.

Team work is very important with this build. If left alone in a lane, Annie is very vulnerable. She can make a GREAT ally early game so stay with your fellow laner and make sure to guard their back. You can get fed easily early game this way. By Mid Game start looking for ways to summon Tibbers into the middle of a team fight to reverse the outcome and help your teammates push. By this point you should be a little difficult to gank so you can venture off if need be to solo farming. By the time you reach Late Game, you should have at least the first 4 items and be building the 5th. Be wary of charging into team battles where the enemy champions have most of their health because they can focus you to keep you from summoning Tibbers without taking much more damage than they already have

Your Q and W abilities are an absolute must to achieve efficient farming. Level them first if you want to survive. Don't try to jungle until at least mid game to keep from getting killed.

Annie's passive ability, stun, must be used with absolute timing. One misfire and hitting a minion instead of a champion with stun can render Annie very vulnerable to retaliation. If you are a couple stacks away from getting the stun, cast your E ability a few times to get it, even if you don't need it. The extra mana usage will pay off later when you stun a champion and get the kill for extra gold.