Head on over to ValveSoftware.com to participate in their Linux survey, which is used to find new Linux gamers to get involved with the beta testing process. "We're looking for Linux gamers to install and test our new Steam for Linux client. We are primarily interested in experienced Linux users. In order to take the survey, you need to first login with your Steam account to link your response with your Steam ID."
Valve will be allowing in around 1,000 people plus they are also preparing a beta for next week's Ubuntu Developer Summit in Copenhagen -- they also have a Valve Ubuntu presentation prepared. It's expected after a couple of weeks of the "closed" beta testing, the Steam Linux client with various Source Engine games will be opened up to more.
Last but not least, Valve has also setup a Valve beta access discussion area for the Linux client on SteamCommunity.com.