Calcite

You can procure a calcite block by simply breaking it with the help of a pickaxe. If broken without a pickaxe or any other tool you will not get the block as it will just disappear without dropping anything. You can find calcite underground around amethyst geodes. They are a naturally generated part of the geode outer layers which are made of smooth basalt and calcite, with smooth basalt being the outermost layer. Calcite can also be found in the snowy peaks of mountains in strip formations.

An amethyst geode (via Mojang)

Currently, calcite blocks cannot be used for any specific things other than decoration.

Calcite is a brand new block, so its uses are limited as of right now but you can look forward to seeing what Mojang decides to do with it in order to make it more useful for players.

Q. Is it easy to find Calcite?

A. Currently, the only way to find calcite is by finding an amethyst geode in an underground cave system.

Q. Can you craft Calcite?

A. No, you cannot make calcite with a crafting table or a furnace.

Q. Can villagers trade for Calcite?

A. Yes, mason villagers will sell you Calcite if it is available.