While Microsoft is taking its own sweet time in making it usable on the PC without wires, you can easily game on your computer with an Xbox One controller that's wired in.
In addition to a computer with Windows, all you need is a Micro-USB cable (used for charging most Windows and Android smartphones), an Internet connection to download the required drivers, and, of course, an Xbox One controller.
1. Install drivers
Boot up your PC, connect to the Internet. Download and install one of these driver packages depending on your version of Windows:PC drivers for 32-bit WindowsPC drivers for 64-bit Windows
2. Connect the controller
With the drivers installed, plug in the Micro-USB end of the cable to the controller and the USB end of it into your computer's USB port. If it works, the controller will vibrate. If it does not vibrate, try another Micro-USB cable and/ or a different USB port.
That's all you need to do to get your Xbox One controller working on the PC.
If you plan on using the same controller with an Xbox One, you will need to re-sync the controller to the console. You can do this by holding the wireless sync buttons on the console and controller at the same time or attaching it to the console via Micro-USB cable.