Compared to 6 mages, 3 mage comps are much more reliable and Brand is the natural carry for any 3 mage build. Using 3 mages also allows you to use transition units to hold items for Brand.
The comp can transition quite easily, but Brand requires lots of Needlessly Large Rods to become a potent late game carry. Starting out with early ocean and inferno units will also help ease the transition.
Early game you can use whatever units you find to transition.
Since this comp relies on an upgraded Brand carry, you will need to build your economy in the early and midgame using good early units like woodland, while holding onto your units that will make the endgame comp. After level 7, roll down to find your Brand.
Before you find Nami, you can use Syndra to keep 4 ocean buff, and remember if Qiyana is mountain you can use her along with Taliyah to win some early rounds.
If you are able to make Mage's Cap during your game, you can also transition into 6 mages with Mage Malphite instead of Thresh and Nautilus.
Nami can also be a potent late game carry, and if you have enough Rods you can place your Morello on Nami instead of Brand to hit more units.
Since this comp only requires a few core items for Brand, use your remaining items on solid picks like Zephyr or Guardian Angel.