Get Plasma Bigscreen
Plasma Bigscreen is now released as a part of KDE Plasma, and is available as a package in Linux distributions.
Some distributions ship dedicated Plasma Bigscreen images, providing an out-of-the-box experience without any extra installation steps.
You can check the status of Plasma Bigscreen on the Matrix channel or the KDE Invent repository.
postmarketOS
PostmarketOS (pmOS) is a pre-configured Alpine Linux that can be installed on smartphones, SBC's and other mobile devices. View the device list to see the progress for supporting your device.
Plasma Bigscreen is currently only available in the nightly repository that tracks Plasma development. Follow the setup guide after installing pmOS regularly (ex. with Plasma Desktop).
Fedora
Fedora provides the plasma-bigscreen package in their repositories. There is no dedicated edition just yet, so you will need to start from another (ex. Plasma Desktop).
KDE Neon
KDE Neon has a development version of Plasma Bigscreen in its repositories. This image, based on KDE neon, can be tested on x86-64 based computers.
Building it yourself
Developers use the kde-builder utility to build and develop Plasma Bigscreen on most distros (with reasonably new dependencies, like Arch and Fedora). See the wiki page on how to set this up.