This is the way I play brand, I really don't know what to write here, just try it and comment how did it go.

These runes are great because at about level 10, if you don't already have deathcap, you'll still have about 80-90 ap with just blasting wand.

Many people take +5% exp gain in utility, but I find it quite useless. Majority of the games I lane in mid and with brand, it's really easy to kill your opponent and take the mob kills, so you don't need the exp boost to outlevel the enemy.

Items are quite balanced for quite a good amount of dmg and survivability. I have listed just 5 items you need to buy and the 6th one is your own decision, though I would recommend buying either Zhonyas Hourglass, Abyssal Scepter or Deathfires Grasp.

Sear will be mostly used just to stun, not to do dmg, pillar of flames does great aoe dmg, so you'll be doing huge dmg in team fights as you max it out fast.
In lane, I usually use conflagration -> sear -> pillar of flames -> ignite -> pyroclasm.
Sometimes, when you are helping other lanes, 2 enemy players fall back to their turret, then Pyroclasm + Sear, followed by pillar of flames can be a great way to get a doublekill and a turret kill.

Ignite is one of the best summoner spell you can choose as brand. You already have a dot from every ability and that + ignite has got me kills hundreds of times.
Flash is mostly used in team fights, just blow out all your abilities and flash away, but keep attacking them from distance.
Also, flash is a perfect spell to be used in mid when your opponent is down at 60% and less hp, just flash, stun and kill.