I honestly have no idea other than it involves Blaze rods.
Read the wiki though, normally really good
http://www.minecraftwiki.net/wiki/Brewing
edit: Looks like you need bottles of water, and then make one of 4 'primary potions' with the base ingredients. Awkward potions (made with nether Wart) seem to be the base for the most useful ones.
Then you take the resulting potion and add in another ingredient to give it an effect (for example: glistering melon is for healing, sugar for swiftness). Finally you can do a final combine with glowstone or redstone to increase the potentcy, or gunpowder to make it throwable (for negative potions, I guess).
From reading, it seems you put the ingredient in the top slot and water bottles in up to 3 of the bottom slots, I assume this allows you to make multiple potions at once.