I'm unsure on how it works on the PlayStation (As you mentioned wanting to do this on a PlayStation) however I doubt there will be much difference to how you do it on Xbox One. But anyways how you do it on Xbox One is you just go onto the "Snap" feature, then you select "Game DVR". From there you can begin to record the game that you're currently playing, however you'll need to actually be playing the game in order for it to record what you're doing, just simply double tap Left 2 times on the D-Pad and it'll take you into the game and the Game DVR will already be recording, once you've captured the footage you simply double tap Left 2 times on the D-Pad again and go to "Game DVR", there you can end the clip. Once the clip has ended you can edit and upload it via the Upload Studio.
Hopefully this will sort of relate to PlayStations way of doing it, if you have any troubles with it I'd just go on YouTube and look for a tutorial!
Oh and you can't do this on old generation consoles, only on PS4 and Xbox One.
If it's on your File Share I can just view your File Share and download the clip from there.