You need to get to a pretty tall spot, and look around for the Nether Quartz Ore. Then go to it and use your pickaxe to mine it; each ore should drop 1 Nether Quartz (more if your pickaxe is enchanted with Fortune).
 4 Nether Quartz pieces put in a square in the crafting table give you 1 Block of Quartz, a whitish block. Quartz Blocks are only used for decoration; they have no unique characteristics.


A way to search for Nether Quartz Ore is to create a corridor inside the Netherrack. Every set amount of blocks, create smaller channels of 4-5 blocks to the sides of the main corridor. This exposes you to the most amount of blocks, increasing your chances of find Nether Quartz Ore.
Find Nether Quartz Ore. Nether Quartz Ore spawns fairly commonly in the Nether, but the blocks aren't very close together.
Collect a lot of Nether Quartz.
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