A simple way to get some system information is uname -a, but this only tells you about whether you are using GNU/Linux and the version of the linux kernel.
There are several possibilities to determine the distribution and version.
cat /proc/versiongives you the kernel version, the build, release, and distribution you are running.
On the beowulf cluster:
Linux version 22.214.171.124-73.fc9.x86_64 (mockbuild@) (gcc version 4.3.0 20080428 (Red Hat 4.3.0-8) (GCC) ) #1 SMP Tue Dec 16 14:54:03 EST 2008
On my desktop at work:
Linux version 2.6.27-9-generic (buildd@yellow) (gcc version 4.3.2 (Ubuntu 4.3.2-1ubuntu11) ) #1 SMP Thu Nov 20 22:15:32 UTC 2008
You can also list the /etc/*release,
On the beowulf cluster I do
cat /etc/*-releaseand I get: Fedora release 9 (Sulphur)
On my desktop I get, also on the same command: