To adjust the brightness of the keyboard, select F1 to dim or F2 to brighten, or turn off the backlight entirely, select F1 until the keyboard icon disappears.

To turn off the backlight in the Surface keyboard, press the key next to Esc key (see the image below). If you keep on pressing this key, you can see that the backlight intensity goes down until it switches off completely. If you want to turn it on, you can press and hold the key next to the key which you used to disable the backlight.