You'll need a Facebook account to do this. You can only use gameplay that you have recorded and saved to your PS4, any streamed gameplay won't be saved to the console. You also have a maximum recording time of 15 minutes.
4) Fill out all the relevant information (you also have the opportunity to edit your clip at this stage). You can set the sharing privacy in the global PSN settings, or upload privately and adjust them later on Facebook, but it needs to be open to the public to allow the next step to be successful. When you're happy, click 'share'
Go to http://downvids.net/
This allows you to enter the URL of your facebook video post. Paste it in and, if you want the best quality, choose the 'full HD (1080p)' option. This will then scrape the video from Facebook.
Right click on the download button and you can save the file in .mp4 format to your computer.
And here's the final footage to give you an idea of quality.