Saph 2 pots
Rod of Ages
Void Staff or DFG
Another RoA, BV, or Guardian Angel
If you're in a REALLY bad game, skip Mejai. Annie can generally keep a good stack even in a losing game though unless they have a seriously fed Shaco or something.
WQQWQR then R>Q>W>E. Some people like an earlier point in E at like level 7 for charging stun. Using shield while Energized is up will build a hidden counter for your next stun after you use a damaging ability.
Try to get mid. Early game last hit with Q and your godly ranged normal attack. When a stun is up move up to harass/deny your opponent. If they eat the stun land a W then go back to last hitting with Q. When you hit level 6 you are one of the most threatening champions in the game. Get a Mejai, then kill your opponent mid or push him out, then start going ganking.
Late game Annie is basically about timing your stun. If they have someone like Twitch or Katarina you probably don't want to burn your combo until they appear and do their scary stuff unless you are absolutely confident in having a teammate do it. Try to always make sure their carry is affected in some way by your stuns. Use shield while Energized is up to build up for a second quick AoE stun after tibbers - this takes practice.