Hi, this is my guide to brand. It is also my first build I'm posting.
Personally I find Brand has a great early game damage output, however his AP scaling on his abilities are low and he has no escaping power when he is ganked. This is my personal build for him most the time, but it does vary depending on the teams.

My mastery is pretty basic, I take Good Hand over Perseverance simply because it is better. If you do not know why then I am not up to doing the math. However I find 10% death time much better than MAYBE 2 extra point to regen.

As for runes, these are the runes I have for almost all my castors. I do not have a rune setup for every hero I play and I find this setup to be rather balanced for my liking.
The explanation behind the rune choices tho I will say briefly:
MPen Marks, always good to have 10 Mpen early game as with that + Sorc boots = no MR for a lot of heroes who do not get any MR.
MP/5 Seals/glyph allows for me to harass with (but not constantly spam) abilities without the need of heading back.
CDR Gylphs, a slight CDR boost early game is nice for me.
AP Quint, for Brand I don't get much AP for him till later in the game, so having a bit from rune helps his damage.

1v1
E>Q>W
I generally do not use his ult on 1v1 unless they are dead from the ult for sure. OR if they are by a few creeps and then I pray it bounces to the target a second time.

Team fights
If enemy team is clustered
Q>R>W>E

The goal is to hit one with Q then throw the ult and pillar down. And hitting the blazed target with E to for the AOE and to set everyone to blaze for R and W to finally proc.

When Enemy team is not in a cluster
W>E>Q (casting order) and skill set should hit E>Q>W, this is very similar to 1v1, as if the enemy is not clustered together this set does more damage. Umm try not to use all your skills if the "first" enemy is their tank. He's just bait.

My note on the side:
Chances are people are thinking "what the heck is this idiot doing his points are all over the place". I will explain my logic behind it.
First I get sear first because it allows for checking bushes as well as it has a longer range if you can do the skill shots. (if not then you can op conflag first) Also my early game harassing with Brand is to poke with sear and let his passive do its run.
I pull points into pillar because from one hit wise Brand does the most damage from pillar after your target is blazing, assumes hitting with the pillar.
Lastly I do not focus one ability after pillar because I prefer the slightly shorter CD from lvling sear and conflag. The slightly shorter CD from sear can sometime mean a difference in getting a second stun or not, and from that reason alone I put points between the two and not just conflagration.

Also if I find my sear isnt landing very well alot of the time I would swap the points between W and E as Conflagration will never miss.

My choice are Flash and Teleport.

Flash to get out from ganks, as Brand does not have a good escape otherwise. It is also nice to flash in sometimes to land the final hit that you otherwise can not catch up for.

Teleport simply allows for less downtime and the ability to help other towers if you need it. With wards its also help to set yourself in a ganking location or in front of a running enemy champ.

I start with Doran's ring as it gives HP, which he is low on, mana and AP for a great early game item.

Personally my build stacks MPen and one of the main reason is because Brand's AP Ratio is not very good. So the first item I complete is Sorc boots and Haunting guise to punish any enemy carries that do not get MR early on. We all know Brand has a very high damage output early game already so I forgo some AP early on.

Both the Haunting Guise and Rylai's provide great HP boost to help Brand survive, not only that but the slow from Rylai's can mean some enemy hero can never catch you by themselves with the slow + your occasional stun. Not to mention the blaze keeping heroes slowed for extra length.

If the game goes on long enough that there is enough gold to replace the Haunting guise I usually replace with an item depending on the situation.
Some of my Choices include: Abyssal Scepter (If they have a really heavy MR tank), Banshee's Veil, Morello's Evil Tome (can be replaced with blue buff!), and Zhonya's Hourglass (If they have global ults other effects that can be dodged with activation.

Things I Did not mention is wards and potions. Warding is important, although I did not list buying wards THEY SHOULD STILL BE Bought. As for potions I buy them depending on how I do. If I am taking more damage than I like I will stock a few HP pots and one mana pot. When I am not taking too much damage while laning, then I try to keep one HP pot and a few mana pot. Because my build LACKS MANA!

Farming with Brand is easy. Pillar the creeps and follow up with Conflagration, with the correct placement most of the wave is dead. Although early game I would not suggest pushing lanes too much as Brand is easily ganked. This method requires alot of mana, which the build does not support. So last hits are really the better choice unless you need to clear a wave or a stack of minion.

For Laning
Solo Mid:
I personally like to harass with sear. It has a great range and lowest mana cost of all the abilities.
Melee Heroes are Conflagrationed when he goes in for the minions. If champ is agressive, sear then run back. Soon he will not have the HP to keep charging you and you are free to deny minions. (Warding when denying is HIGHLY suggested or risk being ganked)
Range Heroes requires more targeting and generally aimed at when running around creeps. Pop shots are taken.
For anyone having problems searing, I would recommend putting points in conflagration instead of pillar. This way you can harass by blazing a minion, then conflagration to enemy hero. Doing this will lower the damage you do in a combo against a single enemy champion, but should not reduce your ability to farm minions.

In Summary, I type alot.

Real summary, Brand is a great early game nuker with a bad AP Scale so I almost get no high AP items besides Deathcap for him. Usually The items I end up getting are more for the unique abilities than for damage.

I'll be happy to hear feedback regarding the build. And also my wordiness.