Find the "release" file and print its content:
$ ls -ld /etc/*release
$ cat ... # the *-release file
This is valid for most Linux distros, such as CentOS, Debian, Gentoo, Fedora, Ubuntu, Mint ...
Or get the information from the login screen:
$ cat /etc/issue
For Debian family distros, like Ubuntu, Mint:
$ ls -ld /etc/*version
$ cat ...
The final solution is lsb command, but not all distros support it.
$ lsb_release -a
Ref: How do I find out what version of Linux I'm running?