While there is unfortunately no native YouTube app available on the PlayStation 4 yet (it's coming, but no date yet), NeoGAF user "S¡mon" has shared a workaround to get an "almost exact replica" of it on your console. And the best part is, it's incredibly easy.
Simply open the PS4's internet browser and go to "http://www.youtube.com/tv". It's as simple as that.
Other steps you can do for a more "optimal" experience include using the Square button to go full screen and bookmarking the page for quick access (or if you go to the page enough it'll show up on your Frequently Used Pages list). You can take things a step further by pairing your mobile device (smartphone or tablet) and using those to select a video while watching it on your television.
Unfortunately, the layout is nearly identical to the Xbox One YouTube app which isn't the optimal experience, but at least it's a functional workaround while we wait for a more official YouTube app to arrive.
