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The main article can be found at Minecraft Wiki: Nether Star.
The Nether Star is a Vanilla item obtained by killing the Wither boss. It is used in crafting end-game items, such as the vanilla Beacon, and in some mod items such as the Supercharged Gravity Gun, Miniature Black Hole, and Advanced Nuclear Information Reader.
Since the star is consumed in each recipe, you need to obtain one star for every recipe you wish to complete, meaning you must kill multiple Wither.
The Tome of Alkahest from Xeno's Reliquary provides an alternate method which requires one nether star to begin with, but outputs two nether stars. Additionally, the Uncrafting Table can be used to obtain Nether Stars without killing the Wither by exploiting the lightning-based conversion of a regular Gravity Gun into its Supercharged version.
With Xeno's Reliquary
With Extra Utilities
Note: The following recipe only works on Peaceful difficulty, and is intended to make the Nether Star obtainable on Peaceful.
Aside from crafting recipes, Nether Stars are also used in some Thaumcraft 4 items such as Ichor, a Thaumic Tinkerer. Also, it can be converted into 10,000,000 EU in a Magic Energy Converter, enough to fill up an MFSU completely. It can also be used in a Mutator for a 100% chance of a bee mutation.
Thaumcraft 3 recipes, *outdated* as of the new modpacks