Google Play is not a downloadable application, but is a competing marketplace that comes pre-installed on supported devices. There is no way to manually add your phone or tablet to Google Play’s supported device list, and you will not be able to use the Google Play website for your device if it is does not come with the Google Play application already.
Do consider if buying applications from a device that is not officially Google Play-enabled as refunds or access to redownload applications again may not be permitted.