Brewing is the process of obtaining potions.
As fuel for Brewing Stand is used Blaze Powder (can be crafted from Blaze Rod). Water Bottle is a basic for all potions. You can craft Water Bottle to basic potions that has no any effects - Mundane Potion, Mundane Potion (extended), Thick Potion, Awkward Potion, and to one potion with negative effect - Potion of Weakness.
Awkward potion is a base of most potions. Awkward Potion can be obtained through brewing using Nether Wart as an ingredient.
Mundate Potion can be obtained through brewing using Sugar (and other ingredients such as Ghast Tear, Spider Eye etc.). Mundane (extended) Potion can be obtained through brewing using Redstone Dust as a base ingredient.
Thick Potion can be obtained through brewing using Glowstone Dust as a base ingredient.
How to Start Brewing and Brew Basic Potions