Sorcerer's Shoes
Okay Kitty kat, these are important for a pretty obvious reason.
catalyst the protector Catalyst the Protector
This is a wonderful item to build right away. It grants you a nice mana and health bonus which will allow you to stay in lane much longer. It's passive grants you both mp and hp regeneration, adding to your lane ability. You'll want to build this into the RoA as soon as possible in order to get the most out of the RoA early game.
Rabadon's Deathcap
Look at this hat. Do you see it? ****ing remember it for LIFE. Why? Because this dirty bastard can pump your AP up so high you'll be walking on sunshine.
****ing SUNSHINE man.
Void Staff
What? They're building magic resist? Well then grab this and ram it in their ***es. This nice little item will become your personal sex toy of penetration. Spell penetration that is.
Rylai's Crystal Scepter
Maybe your opponent is getting away too easily. Maybe they're turning you into soup with half a glance. In either case this little puppy will turn all of that around. With a chance to slow on ability use as well as a *****in amount of hp, you can't go wrong with a Rylai's
Zhonya's Hourglass
Okay, let me level with you for a second. Getting 100 ap out of an item is pretty ****ing cool. Getting 50 armor along with it is, well, pretty ****ing cool. But when **** is really going down and your *** is up next on Warwicks dinner plate, popping that active ability is probably the coolest ****ing thing you can do. Ever.

Alright, let me show you this map.

You see that?
That's a damn good looking map.

As an AP champ, you will usually be going down the middle lane.

Alone.

BLUE CIRCLES. These two bushes are very dangerous if you pass half lane. Why? Because inside every bush is a jungler waiting to punch you in the baby maker. If you find that the enemy jungler is in your lane a lot, then grab some wards and throw them here.

GREEN CIRCLES. This is where the grand blue buff golem spawns. The blue buff lowers your cooldowns and increases mana regeneration by a lot. Your jungler should usually be nice enough to let you have this buff early game, so watch for it.