Valve has made the the Steam for Linux beta client available to the general public, if you're running Ubuntu 12.04 you can download the client over here. Users of the closed beta test are advised to upgrade to the latest version as the new release contains several bug fixes, including fixes for Team Fortress 2 and Cubeman.
The Steam for Linux beta program is now open to the public! In order to participate in the beta, you must download the latest Steam Linux client (found here) or upgrade your existing Steam for Linux client to the latest version.
In addition, we will now track Steam for Linux client bugs using GitHub. This provides a better interface for tracking bugs than the forums used in the closed beta. The Steam for Linux repository (currently empty) is public, allowing anyone with a free GitHub account to create a new issue and edit or track it and search the existing bug database. The repository contains a readme file (README.md) detailing how to create a new issue (it describes the same format used in the closed beta).
The team will continue working through existing issues in the forum but it is strongly recommended that any new issues be entered using GitHub's issue tracking interface. The sub forums will remain open so that people can join/continue existing discussions about the Steam for Linux client.