Collecting Amethyst Shards from Amethyst Crystals is quite easy because you can track the crystals. That said, these crystals are pretty illusory, even in Minecraft terms. Amethyst crystals can only be generated inside a new type of small cave generation called the Amethyst Geode.
The Geode is made up of Geode Blocks, which are a type of block that cannot be obtained with any tools currently in the game, not even the Silk Touch enchantment.
You can recognize a geode block even if you don't see any crystals yet by its unique purple color and shiny design, even if it doesn't emit light.
Image via MojangYou can only find amethyst geodes underground, as this is a type of cave generation. That said, it is extremely small, and since there is no doubt in the outside world as to its location, as with the lush caves and their acacias, finding one can seem nearly impossible.
That said, there is a way to know there's one nearby, even if you don't have any visual signs yet. When you are in or near an amethyst geode, you will hear the sound of bells ringing. It's not clear if these radiate from blocks, crystals, or the location itself in the same way the mine shaft had minecart sounds.
Once you've located the geode, you can harvest Amethyst Shards which can be used to create the all-new Telescope Tool. It remains to be seen whether the fragments will have other uses as well.