To connect an Xbox 360 controller to an Xbox One, there are adapters. Unfortunately, these adapters cost as much as a new Xbox One controller.
I will show you a free technique to do it without an adapter. For this you need a wired Xbox 360 controller and a computer.
You have to go to the Microsoft Store and install the application "Xbox console companion“.
After starting the application, you need to log in to the Microsoft account you use on your Xbox One.
Once on the home page of the application, click on Connect at the bottom left of the screen. Then, in the "Add a device" window, click on "Connect" to choose your Xbox One. You just have to wait a few seconds for the connection.
Connect your controller to your computer through the USB port. On the application, click on "Stream". A connection page with the Xbox One will appear. Wait a few seconds.
The connection is finished. On your computer, you see the same thing as on your Xbox One. Now you can use the controller on the Xbox One.