Binary packages are available for some Linux distributions. You can also compile manually from source (requires CMake 3.1 and Qt 5).
skyjake's PPA has Doomsday builds for a number of versions of Ubuntu. The Ubuntu repositories should also have stable releases of Doomsday.
Check Debian's repositories for binary packages.
Doomsday Engine package for Gentoo
Binary packages for Doomsday are available in the openSUSE repositories.