Installing

You need:

a 64-bit PC running Linux with snap (Ubuntu has it already)
a Microsoft account that owns Minecraft: Java Edition (sold as Minecraft: Java & Bedrock Edition for PC). Without one, the launcher offers the free demo.
an internet connection the first time, to download the launcher and the game

From App Center (Ubuntu)

Open App Center and search for minecraft. Choose Minecraft Installer by James Tigert.
Press Install and type your password if asked. Once it's installed, the button says Open.

The same page is on the web at snapcraft.io/mc-installer.

sudo snap install mc-installer