One enterprising modder has engineered a solution for using an Xbox One controller on a PC.
Microsoft has said it will provide official drivers to enable the new controller on the PC in the future, but it has not said when these will be released--until then, this unofficial solution will work nicely.
The modder, Lucas Assis, said in a YouTube video that it took him about a day's work to engineer the workaround. There's a few steps involved to get it working, but any confident Windows user should be able to get it up and running in about 10 minutes.
Assis provides all the relevant information in his tutorial on YouTube.
In short, the workaround requires you to install a set of drivers and software to fool your PC into assuming a regular old Xbox 360 controller has been connected to the machine.
A similar solution--of tricking Windows into thinking an Xbox 360 pad has been connected--has been made available for the PS4 for a while now. Unlike the actual DualShock 4, when using the controller on the PC you can even disable the Light Bar.