Difficulty: 6/10
Mobility: 0/10
Crowd Control: 5/10
Toughness: 0/10
Utility: 0/10
Damage: 10/10

Short Guide:

One day, I will also upload a short Galio Guide on Yotube: https://www.youtube.com/channel/UCv64msoQzSvy78RxuqKzn_w

2.1) Strengths:
+Huge AoE Damage
+Effective vs Tanks
+Some Poke
+Good Lane Pressure
+Can Snowball
+Good Scaling

2.2) Weaknesses:
-Bad Escape
-Skillshot Based
-Often Steal Kills
-No Utility
-Bad Peel

3.1) Boots:
Sorcerer's Shoes: Normally this are the best shoes, because magic penetration is very strong against champions without a lot of magic resistance (like an ADC XD).
Ionian Boots of Lucidity: Against a team with a lot of magic resistance. Only when you have 30% or less cooldown reduction. But often the other boots are better.
Mobility Boots: A lot of map pressure, take them for faster roams.

3.2) Core Items:
Eye of the Watchers: You are the supporter, you need to place a lot of vision.
Rylai's Crystal Scepter: Important cheap item. Your AoE Damage and the slow synergize very good. The slow helps to hit the skillshots.
Liandry's Torment: Useful against tanks (% damage) and carries (magic penetration).

3.2) Damage Items:
Rabadon's Deathcap: Strong late game item, normally you should take it after Void Staff.
Void Staff: Strong item, usually take it directly after the core items.
Luden's Tempest: The stats (Ap + Movement Speed) are useful, but Brand don't really need the additional waveclear/the new passive (not as useful in late game, when you can buy this item).
Morellonomicon: Useful against champions with a lot of heal (e.g. [Soraka).
Mejai's Soulstealer: Sometimes useful when you are snowballing the game (mostly there's a better option).
Rod of Ages: Very situational and often a bad chose.


3.3) Defensive Items:
Abyssal Mask: Against a lot of AP.
Zhonya's Hourglass: Often a good choice, if you do the most magic damage in your team.
Guardian Angel: Strong late game item, but I prefer Zhonya's Hourglass.
Redemption: Good supporter item, synergize with Rylai's Crystal Scepter.
Banshee's Veil: Against a lot of Ap, but Abyssal Mask/ Locket of the Iron Solari are better.
Locket of the Iron Solari: Strong supporter item, better peel.

Flash: Always take this summoner spell for some mobility. Useful as an escape/offensive tool.

Exhaust: Nearly always this summoner spell is the best choice.
Ignite: Only useful in the early game, when you play with an aggressive ADC.

Brand is an aggressive Support and should poke the enemies with spells and auto attacks. Spellthief's Edge and Bandit give a lot of extra gold. Maybe you should help pushing the lane, but don't steal farm. Build up pressure with pushing, poking, take control of the two bushes, roam to your mid lane or place some wards in the enemy's jungle. Don't go too deep you are very squishy.
-Against a tanky support you should stay save and don't give them a chance to engage on you. Poke him when he's last hitting.
-Against a utility supporter you can often play very aggressive, with level 6 you are normally the playmaker.
-A mage support often has more range and more CC than Brand, but less damage. Don't fight when you missed a skillshot.

The mid game is very situational. As long as you stay in your lane you can follow the early game tips. But don't forget that your strengths are teamfights. Also try to build up pressure around the Drake, Herold and Baron, because your passive deals insane damage to this objects.

Don't leave your Team (they should also follow you when you are going to place a ward) and force teamfights, because Brand has a lot of AoE Damage and can easy carry a teamfight. But stay in the backline and wait with your ultimate until the enemies stay close together. Remember you are squishy don't go too deep.

05.03.2017: Published (Patch 7.4)
16.03.2017: Title form Brand Support Guide | 7.4 to Brand Support Guide | 7.5