To begin the installation process, navigate to https://cygwin.com/install.html and download either setup-x86_64.exe or setup-x86.exe depending on the version of Windows you're using (64 bit or 32 bit respectively).
If you're not sure whether your system is 32 bit or 64 bit, you can open Control Panel | System and Security | System, and look at System type. For example, my Windows machine shows System type: 64-bit Operating System, x64-based processor.
Open the executable file, and you will be greeted by the following Cygwin installation window:
Hit Next > a few times, proceeding with the default settings: