***Disclaimer***
This Build is not for beginners. It requires being good at skill shots. That being said if you are routinely missing stuns please do not vote negative cause you haven't practiced enough. If you cant hit stuns you WILL fail at this build.

***Furthermore***
Please do not vote until you have tried this build. If you have poor results, try again. Also if you have a criticism of this build please post a possible solution (i.e. DONT SAY: Getting Mejai's is stupid, TRY: Mejai's may be a poor choice. Evil tome would probably work better for this build)

This build for brand is based off of some lessons learned form other builds and improvements for given situations. The main focus will be when you are soloing middle, and dont have anyone on your team taking the golem buff.
The Idea is to use the EXP boost from soloing mid to grab the golem buff before anyone on your team, and use the mana regen to keep laning rather than any mana Items. hense freeing up gold for AP based items.
This guide has given me a huge advantage to other AP chars im laning against mid, and helps fill the stacks on Mejai's Soulstealer alot quicker.

I use these Masteries mainly to be able to spam my spells sooner. This with my runes, a 20 stack mejai's, and the golem buff will give you the max cool down reduction. Which basically gives you a 40% increase in damage output.

I prefer to use Flash, and Ignite.

Why Flash?
Simply it gives you some ability to retreat if you need to, but for the most part I use it to chase down low health players as they are running away and turn them into mejai stacks.

Why Ignite?
Most summoners fail to plan (especially early game) for the damage output of ignite. Also it stacks on your blaze passive. So at level 5 you will do 150 damage + 8% of their health over 4 seconds. This will lead to easy one on one kills in the early game.(all game depending on the situation)

other Spells?
Teleport: Good for ganking. I only use if we have a teemo (as he can spam the shrooms making it easy to gank).

Other than Teleport i dont recommend any other spells.

The justifications for the Items I've chosen is as follows:

Meki Pendant : Helps with early mana regen. Even if you are building the Archangels's Staff this will give you more mana over time than the Sapphire Crystal will give you flat out. Will keep you laning till almost level 6 if you conserve mana.

Mobility Boots : This is because of the absence of Teleport in the build. Gives you a huge amount of movement speed when not in combat allowing you to quickly position yourself to get kills.

Mejai's Soulstealer : With this build you will have more AP than most chars of the same level as you have no defense or mana items, so getting kills should not be a problem.

Rylai's Crystal Scepter : This will add insult to injury during mid game. you will already be more powerful that any AP char on the map, but this almost guarantees your stuns and helps your team get kills as well.

Rabadon's Deathcap : This is obvious. Huge amount of AP + a 30% overall increase. If you make it this far the other team is most likely trying to surrender.

Banshee's Veil : will increase your survivability for late game. also will eliminate your reliance on the Golem Buff.

Its simple. If the only choice is between Conflagration Pillar of Flame or Sear chose the first two. Keep pillar of flame one step ahead of you Conflagration, and if your Ultimate is an option pick it. Get one level of Sear at level three. After that wait till you have no other option but to upgrade it.(all you need is the stun)

Reasoning:

Some builds say to go Pillar all the way, but conflagration is the same as pillar as far as damage when targets are Blazed. Also its not a skill shot. In addition it takes less mana. So keep it leveled with you Pillar to maximize damage. (also helps with minion farming)

Start off buying a Meki Pendant and two Health Potion.
Basically just use your Pillar of Flame sparingly for some last hits. Till you get to level two. Once you have Conflagration, use your auto attack to hit minions while using conflag to harass your enemy. Once you hit level three you will have caused enough damage to Conflag, Sear(stun), Pillar, Ignite your enemy for first kill.

Repeat this process using only auto attack to hit minions and Abilities to hit enemies till level 6. You should now have enough Gold (1000g) to get your Mobility Boots, so head over to the blue golem. Use the rest of your mana to get the buff (dont be afraid to use the ulti).

After you get the buff go back and buy your boots. then it will be time to start ganking.

Ok You should now have the Golem buff and your boots. If not keep laning mid.

If your set, Its time to gank. Quickly find a target away from their turret and about half health(if quishy it can be more) run there and kill. Use Flash to get out if being chased. Now just run back and forth using your forest (killing easy neutrals along the way) to find and kill more enemy summoners. Stop in mid lane to push minions away (and farm them) every time you pass. Use the following combos for the circustance.

minion farm:
Pillar of Flame --> Conflagration

One on One:
Conflagration--> Pillar of Flame--> Sear--> Ignite

Team Fights(away from enemy minions):
Pyroclasm--> Sear--> Pillar of Flame--> Conflagration

Team Fights(with minions):
Pillar of Flame--> Sear--> Conflagration--> Pyroclasm--> Ignite(lowest health enemy)

To disengage:
Run until slowed--> Conflagration--> Sear--> Pillar of Flame-->Run again.

If you do well you will be able to buy Mejai's Soulstealer strait out. If not spend the 415 for the ability tome Grab Golem buff and keep at it.
With this build, when you golem buff runs and u get low on mana, youe should be ready to go back anyway. (Also dont be afraid to steal the enemies golem if yours hasn't respawned yet.)

By level 15 you should have atleast 10 stacks on Mejia's Soulstealer and Rylai's Crystal Scepter built. If you have less then 10 stacks becuase of deaths. Then you need to switch to a non-kill dependant build. So go ahead and sell Mejia's Soulstealer and finish Rylai's Crystal Scepter. Then move on to your Rabadon's Deathcap

By this time most of the teams i play against are trying to push a surrender vote. If they dont, It team battle time.

Ok now you need to start working more with your team than for your team. Get them organized and push each outside tower. If the enemy is fairing even with you then just do the outsides, and dont touch inside till all outsides are dead.

Once your ready to really push, make sure your Entire team goes in first (cause you will be target from the start) Once the enemy commits enter and follow the combo list provided for mid game. This will weaken most of their melee for easy kills. Use the Staff to its full advantage for your team by casting all AOE spells first to minimize possibility of escapes. Dotn forget Ignite. It still will help secure kills on the lowest HP guys. Also will limit their ability to heal. (very useful against a Yi)

While this is going on routinely refresh your golem buff and B to build the rest of your Items. If you get to the Banshee's Veil you probably wont need the golem anymore. (and the game will probably be all but over)

I dont know who to give credit to cause i have used a few builds, but this one i have customized to my game play. So, if anyone sees any part of this that looks like something you said before I did. Maybe i read it from you in the past. Maybe not. nothing here is directly from any build.

Pro's:
Allows you to focus early on AP rather then getting mana
Keeps you one step ahead of other AP chars on your level

Con's:
If you cant get kills or die to often the build crumbles
If you dont plan accordingly or watch you buff, you can run out of mana at crucial moments.