Will an Apple keyboard work on a Windows computer?

Basically, Yes.

Apple keyboards are USB keyboards, and all basic functions will work just fine on a PC, with some limitations: the hardware control functions (volume control, brightness control, media control buttons, etc.) will not work, and the modifier keys are marked differently than those on a Windows computer (for example, the [option] key on a Mac keyboard is where the [Windows] key would be on a PC keyboard).