"uname -a" is the right command, but it is not too helpful in determining which Linux Distro you have. It should at least inform you that you are running Linux and not HP-UX, FreeBSD, SunOS, etc.

As for which distro, Linux does not yet have a great way to do this, but it is moving towards a way. See: http://linuxmafia.com/faq/Admin/release-files.html for a good write-up on the current state of affairs.