While we are still working out exactly how to distribute the final Player version to be as easy as possible for the typical end user, this beta includes 2 gzip'd tarball packages: one is for the Mozilla plugin and the other is for a GTK-based Standalone Flash Player. Either will need to be downloaded manually via the Adobe Labs website and unpacked. The standalone Player (gflashplayer) can be run in place (after you set its executable permission). The plugin is dropped into your local plugin directory (for a local user) or the system-wide plugin directory.
Did I just hear a million Linux users yelling "Thank You" or "About time"?"