Step two: Enable USB debugging mode on your phone. If it's running Android 4.0 or 4.1, tap Settings, Developer Options, then tick the box for "USB debugging." (You may need to switch "Developer options" to On before you can do so.) On Android 4.2 and later, tap Settings, About Phone, Developer Options, and then tick USB debugging." Then tap OK to approve the setting change.
Step three: Run Android Root on your PC, then connect your phone via its USB sync cable. After a moment, the former should show a connection to the latter.
Step four: Click Root, then sit back and wait while the utility does its thing. The aforementioned Supreme took all of about two minutes, including the automated reboot at the end.
And that's all there is to it. If you decide you want to reverse the process, just run Android Root again, connect your phone, then click Remove Root.