I have not found a way to have the DS4 natively recognised on the PC, and like everyone else would be very interested to hear from anyone that has.
Meanwhile I followed these steps:
1. Download the Xbox 360 controller driver
http://www.microsoft.com/hardware/en-ca/d/xbox-360-controller-for-windows
2. Download Input Mapper from
https://inputmapper.com/. This is very commonly used, is a safe install (no adware) and works.
3. In input mapper I set up a new profile using the default settings - I suspect that this wasn't necessary. "Emulate virtual controller: Xbox 360" was ticked.
4. Input mapper needs to be running in the background
5. Press the playstation button on the controller itself. A popup appears (I found I could turn this off once the game was running, but it needed to be on at first)
6. Run the game and get to the title screen.
7. Press a few buttons on the controller to have it recognised. Note that touching the track-pad will re-trigger the Mouse and Keyboard settings. Not a biggie.
8. All buttons work as per the prompts - apart from...
Triangle = Y
Square = X Circle = B
Cross = A
In may haste to play the game I didn't test any other ways of setting things up, and I'm pretty sure some of the above steps are unnecessary but they worked for me. YMMV.