This resource can only be found wrapped around amethyst geodes. It has a white layer between the black outer layer and the purple center where you will see the amethyst resources and this is where you will get the shards. But if you are looking for calcite you will have to go through the dark-colored outer layer, the basalt and reach the depth between Y = 70 and the bedrock to find it.
At one point in the search you will find the Calcite layer that contains the Amethyst in the middle. You could first mine the Calcite first and then grab any Amethyst and then get the blocks from the fragments of the already developed groups.
In order to extract the calcite you will have to use a pick, but keep in mind that right now its only use is purely decorative.
That's all you have to know about how to find calcite in Minecraft, so if you got to this point, we hope you can get all the calcite you need and get a lot of benefit from this mineral when there is more to do with it.