If you're on Windows and you had problems installing Cygwin, there is another package that includes GCC called "MinGW" (minimalist GNU for Windows). Download and run the MinGW installer.

Go through the installer and keep clicking the defaults. It will then download and install several other packages. When the install finishes, do Start Menu -> Run... -> "cmd", then:

C:\\\> md tutorial
C:\\\> cd tutorial
C:\\tutorial\> set path=C:\\MinGW\\bin;%path%
C:\\tutorial\> gcc hello.c

And follow the rest of the directions from the first tutorial post, making the appropriate path substitutions and using \ instead of /.

If you have problems downloading through the automatic installer, try following the MinGW "Manual Download" directions. (Just for the "minimum requirements".)