If for any reason you can't or don't want to use one of the previous installation methods, you can still download Crystal in a standalone .tar.gz file with everything you need to get started.
The latest files can be found on the Releases page at GitHub: https://github.com/crystal-lang/crystal/releases
Download the file for your platform and uncompress it. Inside it you will have a bin/crystal executable.
To make it simpler to use, you can create a symbolic link available in the path:
ln -s [full path to bin/crystal] /usr/local/bin/crystal
Then you can invoke the compiler by just typing crystal.