As with all great software, Python has many versions. This text will use the most recent stable version of Python 3. Many computers have older versions of Python installed already, such as Python 2.7, but those will not match the descriptions in this text. You should be able to use any computer, but expect to install Python 3. (Don't worry, Python is free.)
You can download Python 3 from the Python downloads page by clicking on the version that begins with 3 (not 2). Follow the instructions of the installer to complete installation.
For further guidance, try these video tutorials on Windows installation and Mac installation of Python 3, created by Julia Oh.