My first guide :) !!!

Brand is a ranged nuker that can play any lane, but usually mid.
He specializes in AoE damage, and spell combos.
In different situations, you would use different spell combos.

For items, get a dorans ring to help with early damage and mana regen. Next get boots of speed so you wont be slower than other champs, but dont finish it yet. Get catalyst so that you can heal after lvling up. Build Rabadon for a large amount of AP, and finish your sorcerer's shoes. Get Will of the Ancients before void staff, because around that time, you'll need spell vamp. Sell your dorans and buy a banshee's veil to reduce ccs and damage.

Your passive is Blaze, which is a small ignite, and gives extra abilities to your own.
Get pillar of flame first, because it is the only skill with AoE damage, without Blaze.
Max conflagration because it is the most reliable source of damage, and helps spread damage and Blaze.
Get a point or sear in lvl 3, and keep it there, because you'll need it for stuns and it is not usually used for damage early game.
Max pillar, and then sear, and of course your ulti whenever you can.

When using your ultimate, the best time is when enemies are buched up together, or, when there are no enemy minions. Make sure you blaze atleast one of your targets to speed up the fireball.

Flash and ignite are the basic AP summoner spells. I dont find any other summoner spells to be of use to Brand.

When you farm, you generally dont use sear. You want to try to hit all of the minions with pillar of flame, and then you hit the middle minion with conflagration to spread the most damage. Your Blaze will end up killing all of them if your abilities have not. (Mid-late game.)