Firstly, you should choose which video you wish to embed into your website.
Afterwards you will click on the "Share" button next to the like counter underneath the video to the right.
Once you press the share button, several options will appear for sharing your chosen video.
In our case we are going to embed our video, so press the button that says "Embed"
After you press the embed button, press the copy button at the bottom right of the popup window.
In addition, you may also select what time the video starts at by skipping to a specific timestamp of the video. Afterwards check the "Start at" box.
Once you copy the embed link, open your webpage's editor. Then paste the copied data into an empty line. You should have an embedded Youtube video in your webpage.
After you have completed this step, your embedded link should look something similar to this.
From here, you can change the width and height of your video. However, I do recommend keeping the video in a reasonable aspect ratio to ensure that you can still view it properly.
Lastly, I have linked a video on how to perform the same actions to embed a Youtube video into your webpage. Good luck and have fun embedding videos into your webpage!