If you are trying to find amethyst geodes it's easier than you think. To start, you can find amethyst geodes spawning after Y=70 underground and around bedrock levels. You can also find the geodes spawning occasionally on the overworld, exposed both in beaches and underwater.
Geodes will also have an outer layer of smooth basalt, so if you see this block, there is a good chance it's a geode layer. After the smooth basalt will be a middle layer of calcite block, so if you see that after the smooth basalt, congratulations you found a geode.
Along with that, geodes will also have two other layers with the inside containing amethyst growths. These growths will have four stages that start with buds and end last with amethyst clusters.
You can get amethyst shards if you mine these clusters, with at least a stone pickaxe and above. Once mined, these amethyst shards can then be used to make either spy glasses or tinted glass in the game.
If you want to make a spyglass, you will need one shard and two copper ingots. But if you want to make tinted glass, you will need four shards and one glass block.