Note: This was done in Minecraft 1.9 Prerelease 3. The added, useless ingredients that have been in version 1.9pre1 and version 1.9pre2 can now be crafted into various kinds of potions for version 1.9pre3, which indicates that this system may remain mostly the same on release. However, all information is subject to change. In order to even make potions, a visit to The Nether is necessary. Certain required ingredients can only be obtained there:
Crafting table Bottles: Made from glass the same way buckets can be made with Iron Ingots: Three pieces of glass, in a "v" shape. Brewing Stand: Made with a solid row of cobblestone, with a Blaze Rod (obtained from defeated Blaze mobs in the nether) in the middle, one row up. Nether Wart: Only obtainable in the Nether, and mainly in Nether Strongholds Water
Potions are multi-step items, requiring various ingredients to produce different effects. While there are three different type of bases, the one that matters at this time is the Awkward Potion, which is made by using a Brewing Stand to brew bottle(s) of water with a Nether Wart. Up to three can be made, so you may as well not waste Nether Wart and make three potion bases, every time. To start making useful potions, you need non-base potion ingredients. Some require even more steps. Below are details of the non-base ingredients, including what they yield when brewed with an Awkward Potion. Also, the Fermented Spider Eye can be combined with other potions to produce negative effect potions.
Made from refined sugar cane. Yields: Potion of Swiftness With Fermented Spider Eye: Potion of Slowness
Must be obtained from a killed (Cave) Spider. Yields: Potion of Poison With Fermented Spider Eye: Potion of Harming
Fermented Spider Eye
Spider Eye, plus sugar and a brown mushroom Yields: Potion of Weakness
Must be obtained in The Nether, from a killed Ghast. Yields: Potion of Healing With Fermented Spider Eye: Potion of Harming
Must be crafted from a Blaze Rod, obtained from a killed Blaze in The Nether Yields: Potion of Strength With Fermented Spider Eye: Potion of Weakness
Kill a slime to get a slime ball, then kill a Blaze in The Nether to get a Blaze Rod. Craft the Blaze Rod into Blaze Rod Dust, then craft the Slimeball with the Blaze Rod Dust. Yields: Potion of Fire Resistance With Fermented Spider Eye: Potion of Slowness (possible placeholder for another potion)
Note: These potions can also be enhanced into Tier II potions by brewing them with Glowstone Dust (obtained from The Nether), and their length of effect can also be enhanced with Redstone Dust (obtained from main world). Also, without making the Awkward Potion, the (currently useless) Thick Potion can be made from Glowstone Dust, and the (currently useless) Mundane Potion from Redstone Dust.