Valve has opened their Steam for Linux beta program to anyone who is interested.

You can now download the Steam client for Linux and start exploring games available on this platform.

The company is also seeking bug reports from beta testers on GitHub. Valve said:

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.