On OSX, you'll probably need to connect the controller via Bluetooth, then use software like Joystick Mapper to map buttons to the keyboard. On the Mac, it may not be usable at all on the PC, there's a tool for emulating an XInput device using a PS4 controller that works okay, though you'll want to test it on a game by game basis, since games that actually support the PS4 controller (Transistor and Broforce so far in my testing) will then register two controllers from one set of inputs. The bad news is that most games on Steam support XInput controls (used by 360 controllers) and not DirectInput (used by the PS4 controller). On my PC, it even recognizes the audio channel as a bluetooth speaker, so I think I could get PC audio out through the controller.
The good news is that connecting it to any PC (Mac or Windows) is pretty straightforward using guides like this.