Amethyst Geodes are a natural structure that was added to the game in the Minecraft 1.17 update. The most important thing to know about finding them is that you can only find them in the Overworld, and only at levels between Y -64 and Y 30.
They appear to the player as a rounded outer layer of smooth Basalt. Some players mistake Basalt for Obsidian, so be sure to look closely if you come across any dark-colored blocks while mining. Rarely, they might generate with a crack in them, making it so the players can see the purple and white blocks inside. It's possible to find them exposed underwater or in caves as well. Regardless of where you see it, if you find a large, curved structure with a Basalt outer layer, you have found an Amethyst Geode.
To get the Amethyst Shards inside the geode, simply break into it (you must have a Stone Pickaxe or stronger). Once you have broken through the layer of Basalt, you'll enter a layer of Calcite. Break through that layer to find the Amethyst Shards waiting inside!