If you are looking to make either tinted glass or a spyglass in the new Minecraft update, you will need to get yourself some amethyst shards. That said, to get amethyst shards in the game, you will need to find a geode and mine into the inner layer to locate what is called an amethyst cluster pictured above.
This is the fourth stage in the growth cycle of amethyst and is the only stage where you can get a shard from the amethyst, so remember how it looks. However, the most important step to finding amethyst shards is first finding the geode.
To start, you can find these big rock layers spawning after Y=70 underground and near bedrock and sometimes on the surface exposed inside beaches or in the ocean.
If you manage to locate one of these geodes in either of these locations, you can tell it's a geode by its smooth basalt layer, so if it has smooth basalt blocks, good chance it's a geode. That being said, mine deep into the layer, and you can find the shards via the clusters, and to get the shards from the clusters, you need only a stone pick up and above.