This is my first League of Legends build so I hope it's good, just trying too help who want to start playin with him or who want, what I believe is, a easy way to play as Brand. And remember this is just a guide, you can change things depending on how the game goes on, or if it suits you more.
Brand is a great nuker, he is very strong in the early game doing a great damage nuking, but a little squishy and have low life so you will be focused often in the team fights, thats why I build that way so he get a little bit of surviving what make it a easy build to play with this champion, and still be strong in the late game.

To be honest I dont have runes so I believe many of the players would know better then I do, but I made a combination that if I had runes I would make.

Greater Mark of Insight
In combination with your Sorcerer's Shoes and the Void Staff this rune will make a great penetration in you enemies magic resist making your spells more efective.

Greater Seal of Focus
Brand is useless without his spells so i believe it will be of great help, even his cooldown already been fast.

Greater Glyph of Force
About this one i believe it is of a good help for every Ability Power champion after all make your magics stronger and magic is you way to kill.

Greater Quintessence of Replenishment
And for this last one, in my opinion its one of the most inportant runes for Brand, he nuke hard and become out of mana many times, so that will be of good help.

In this build I focus the folowing stats, Ability Power so you boost up his spells, Magic Penetration to do even more damage to the enemy champions, Mana regeneration leting you stand in the lane for greater periods, and life turning you a little more tanker. This way he dont get so easy to kill, in the late game you still have a good amount of AP to give a hard damage, and you get Mana regen so you can stay for a long time nuking in your lane without needing to recall, allso I find Rylai's Crystal Scepter a very good item giving you life, Ability Power, and slowing you oponents making then easier to hit with your Sear and Pillar of Flame spells.
But some times when the game get a little hard I make a little change in the build: after buying the Sorcerer's Shoes you can rush the Rod of Ages and close the Archangel's Staff before buying the Void Staff that way you get more life faster then the other way, but if the game is easy and you are feed I found out the other way very efficient.

About the summoner spells i pick always Flash so you can easy rush in to the enemy or escape if is necessary, ghost may have almost the same effect but I prefer Flash making a best choice in my opinion to sneak without the enemy knowing and gank, and Iginite for securing the kill. But if you find out other spells more suitable do as you wish after all you is the one who is playing this is just a guide.

Talking about Skills for me it's no doubt, focusing Pllar of Flame because it does alot of damage, have a huge range, it have a small delay making it easy to use, it have a litlle of Area of Effect, and it's great for farming creeps. About Sear I pick it only one time for stuning enemies, it's good for scaping when Flash is in cooldown or in combination with it to make a secure scape, also will make one enemy useless for a few seconds wich is always good. Conflagretion is the second to focus, does great damage too, it's easy to cast, but have a leak of range. And Pyroclasm wich must be picked always, after all it is you ultimate spell very effective in team fights does huge damage to the hole enemy team.

He is a good farmer, making the money come easy his spells have a medium cost of mana and theis cooldown's are a little fast. I prefer to do the following sequence:
After using your Pillar of Flame in the radius with more creeps posible all of them will burn, right after that you use the Conflagration spell doing a great splash damage and killing almost the hole creeps around who got hited by both spells. The Pyroclasm is also good for farming but I find out a waste using this spell on creeps because she have the longest cooldown and it's much efficient against two or more champions.

In team fights as you will see he is of a good value, with Pillar of Flame, Conflagration and Pyroclasm he can do lots of damage to many enemy champions at the same time, also with Sear spell he can stun key enemies like Nunu, Katarina, Fiddle Sticks when using their ultimate spell or only stuning a someone who is escaping and a champiom who does lots of damage. But you must be carefull he will be focused many times so take a good use of your Pillar of Flame range and stay in a secure distance.
And for smaller fights I like to do the following steps:
Use you Conflagretion spell to get the enemy burning, you migh also use the Pillar of Flame to set the burn effect on them wich will prove yourself more easy to do in some situations but I prefer to save Pillar of Flame for the last maximazing the damage, after you have him burning cast your Sear spell stuning he making easy for you and your partner to finish the job.

He have a unique passive ability wich make Brand spells very flexible allowin you to maximaze damage: when the fight is one on one, chose to do less damage but opt for a area damage: good wen you have more then one opponent, stun enemies: aiding allies in a kill, stop escaping enemies and stoping some harassing ultimate spells.

Hard damage in the early game, great nuker, lots of damage in area.

Low hp, burn out his mana very fast, useless without his spells.

In the end I see Brand as a great champion, like the others with pros and cons, but he is versatile been of a great use for his team, to be honest I find playing with Brand a little difficult, but he is one of my favorite champions and the things got much easier when I did this build so I hope it will help new players and those who are having difficult with this amazing champion.

Thanks for giving a look on my first League of Legends build I hope it may help.
And remember League of Legends is just a game so be polite with other players and have fun, after all that why all we are playng!