Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Brand is a new champion that was popular for a while, and people are still experimenting with various builds. After looking at a few of the builds on this site, I decided to throw my hat into the ring.
-Magic Pen Marks and Quints are the way to go because Brand's burst damage needs to penetrate the opponent's armor. This allows you to get early game kills and early harassing going. The earlier you can start getting kills, the better you will be when the late game comes around.
-Mana regeneration seals help you both early and late game to cast as many abilities as possible. They are the most important early in the game before you have the archangel staff. Often times, Brand will run out of mana very quickly because of the spamming abilities.
-Cooldown Reduction Glyphs allow you to use the abilities as fast as possible. Imagine pyroclasm anytime you see an enemy!
The Masteries are basic. The only points in the offensive tree build around the spell penetration and the cooldown reduction. The rest of the points go in the utility tree.
You begin the game with the Doran's Ring. This gives you everything you need to put up a great fight in the middle and even get some early kills. The first time you head back to the base, you should have enough money for the Sorcerer's Shoes. Grab them to give you a great deal of Magic Pen very early in the game. Your next trip back should be to get the Tear of the Goddess. Getting this early allows you to fully increase your mana, which will eventually add to your Ability Power when you get your Archangel Staff, which is your next item. At this point, you should have enough mana to last you a while, a good amount of Ability Power, and a very good amount of magic pen. Your next item should be Morello's Evil Tome. It gives you a great boost in cooldown reduction. This way you can use your abilities a lot quicker, and it gives you more of a fighting chance in 1v1 fights. Your last three items are up to you (of course selling your Doran's Ring to open up another spot). I get two Deathcaps and a Crystal Scepter for the survivability, slowing, and massive Ability Power. If you are playing a more tanky team (especially with a lot of magic resist), don't be afraid to get the Void Staff or Abyssal Scepter.
I prefer using Exhaust and Ghost for Brand. Exhaust, with the mastery, will slow them enough to get your stun off and hit them with all your abilities, and it lowers their magic resistance. Ghost, however, is a great all-around ability. It can be used to run away when you're about to get ganked, or you can use it to catch up to someone. Both of these spells are very versatile.