Sometimes you will be given a dedicated server or a VPS and you won't know exactly which flavor or distribution of Linux it is running.
Here is how you can find out when logged in through SSH:
# uname -a
This generally won't tell you as much as you'd like.
# cat /proc/version
This will generally tell you more than you'd like.
Once you know that you are running Red Hat for example, you can get to the point with:
# cat /etc/redhat-release
Or on Debian:
# cat /etc/debian_version
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