How to brew potions in minecraft with the new update?

http://minecraft.gamepedia.com/...om/Brewing

Mainly a few alt. Potion making methods closed and overextension of potions are gone as well. Other than that, no new brews have arrived.

There are two new mechanics:

1. Lingering Potion
Collect some of the dragon's breath with an empty bottle and brew it as an ingredient into any desired potions. The resulting potion acts like a splash potion, except with a lingering cloud of effect. You can also craft this within a ring of arrows to get them tipped.

2. Blaze Powder Catalyst
Brewing now requires Blaze Powder as a catalyst, allowing 20 uses. Keep in mind that the supply is used every time brewing starts.