There is no stable release of Calligra yet, but stable versions of the application can be found in KOffice which is the predecessor of Calligra. For downloads of KOffice see the KOffice Download page.
Usage of unstable version is not recommended by the Calligra team.
Arch Linux provides Calligra packages in the kde-unstable repository.
Fedora is working on packages and expects them to be available soon.
Packages are available in area51
Gentoo has Calligra packaged in Portage, tagged as unstable.
Ubuntu users can get a nightly build of Calligra with the Project Neon, you need to add ppa:neon/ppa to your sources.list and install project-neon-calligra package.
This script installs project neon and calligra:
sudo add-apt-repository ppa:neon/ppa \ && sudo apt-get update\ && sudo apt-get install project-neon-base \ project-neon-calligra \ project-neon-calligra-dbg
In order to run the installed packages you have to logout and choose "Project Neon" from the login screen. Neon always has the latest version, not necessarily the beta releases.
Alternatively, you can use this ppa, which packages only the beta's:
KO GmbH will release a windows build of this beta version very soon. This page will be updated when that happens.