Google up the Black Magic HDMI capture card to see what you are getting into.
No one I know uses that system due to the cost. Google "PS4 video capture" to see how folk do this.
Since I bought my computer a few months ago, I have always wondered how the HDMI Input on my computer would be useful. I'm of course using the HDMI output to connect it to my monitor, but an input?
Like, can I download some kind of software that would allow me to plug in my PS4 and capture some footage?