To make YouTube go in the corner of your screen, you can use the Picture-in-Picture (PiP) feature available on certain web browsers and operating systems.
On Google Chrome, navigate to the YouTube video you want to watch and right-click on the video player. Choose "Picture in Picture" from the contextual menu that appears. The YouTube video will then detach from the page and float in a small window that you can move around and reposition on your screen.
On Safari, click on the PiP button available on the video player when you hover over a YouTube video. This will allow you to detach the video player and move it anywhere on your computer screen.
With the PiP feature on your operating system, you can also adjust the video player's size, mute, or play and pause the video without having to click through to the YouTube page. To exit the PiP mode, just click on the X button placed in the top corner of the video player.