Let me just start off by saying brand is in my opinion the best AP caster in the game. He can carry ranked matches if played right, has multi-target spells which are great for team fights, and has great damage output throughout the entire game. I won't go into much detail about runes, masteries, etc. However i will try to go into more detail about his skills/strategy.

For runes, get magic penetration marks, flat AP glyphs, mana per 5 or cooldown reduction seals, and health quintessences.

I chose the standard 9-0-21 masteries that almost any AP caster uses, with magic penetration in offense, and regeneration in utility. I strongly suggest using these not only for Brand, but any mage in general.

I like to start off with a Doran's Ring for the AP, health, and mana regen. Wait to recall until you can afford tier 1 boots and a blasting wand. Next, build your boots into sorcerers shoes. After this try to finish your rabadons ASAP. After rabadon's build Rylai's Crystal Scepter for the AP, health, and awesome passive it gives. Once you have your Rylai's, go straight for a void staff, which will make your spells hit much harder, especially on enemies stacking magic resistance, which they will if your fed. This is the core build, and after this you can get any item that gives AP. I recommend building Morello's Evil Tome, because of the cooldown reduction, followed by a Zhonya's hourglass or Deathfire Grasp. However, you could also go for some survivablity by building a Banshee's Veil before Zhonya's, that way you will have some more armor, magic resist, health, and both of their great passive abilities. These last two items are your personal preference, however.

W>E>Q>W>W>R>W>W>E>E>R>E>E>Q>Q>R>Q>Q>
Put your first point into Pillar of Flame, hen one point in your Conflagration and Sear. You can choose to put a point in Sear or Conflagration first, depending on your playstyle. However, i recommend putting a point in Conflagration first. Once you have a point in each skill, max out Pillar of Flame first, followed by Conflagration, then Sear last, putting a point in Pyroclasm whenever possible.

I always use Flash and Ignite on brand, Flash to make quick escapes or get in position for a spell burst, and ignite for the massive true damage it deals, and when stacked with Brand's passive, can really burn someone's health down. However, other options include ghost and exhaust, just depending on your personal preference.

Passive: Blaze- Makes all of Brand's spells leave a burn on enemy champions, taking a percentage of their max health each second (ablaze). Great passive, leaves a mini-ignite on enemies at no cost. Additionally, targets that are ablaze take special effects from Brand's other spells.

Sear: A skill shot that hits the target and deals good damage, stunning the target if they are ablaze. Put only one point into this skill early for the stun, and max it out last. Can be used to get off a stun lasting for 2 seconds, to ensure the kill or make a quick getaway.

Pillar of Flame: Brand's best ability besides his ult. AOE spell that hits all targets inside the area of effect. This deals 25% bonus damage if the target is ablaze. This spell hit extremely hard all game, especially if they are ablaze. Max it out first, and use it to harass or farm minions.

Conflagration: Brand's only lock on ability besides his ultimate. It instantly hits the target with decent damage. If the target is ablaze, I max it out second. In a 1v1 situation, I open with it. In team fights, use it last so it hits almost every enemy champion, since most of them will be ablaze.

Pyroclasm: Brand's ultimate, launches a massive fireball at an enemy which bounces to nearby enemies, up to 5 times. This spell does amazing damage, and is great for team fights because it bounces, dealing massive damage to every champion it hits.

In a 1v1 situation, your standard spell combo should be Conflagration>Sear (for the stun)> Pillar of Flame (25% increased damage)> Pyroclasm> Ignite to finish them
This spell combo is only if you fully commit to getting the kill. To harass early game, simply hit enemy champions with Pillar of Flame, which does very good damage early game.

In Teamfights: If a team fight starts, stay towards the back, throwing spells whenever you can, but making sure you dont get focused. Your spell burst in a team fight should be Pyroclasm (which should hit almost every champion)>Pillar of Flame (25% increased damage)> Conflagration (which will spread)> Ignite who ever is still left. Sear is not a great spell to use in team fights, since minions could easily get in the way of it, and its single target. Only use Sear to get a stun off on anybody trying to run once the team fight is over.

Pros:
- Great Damage throughout game
- 3 multi-target/AOE spells
- Has a stun
- Amazing passive

Cons:
- Item dependent
- Runs out of mana easily early game

Brand is a great AP caster, who does good damage, especially in team fights. He can carry games, even ranked, and is completely unstoppable, especially when fed. I would recommend playing him, and please try the build out before voting :) Good luck!