So let's say you want to make a website or a page on a website that contains a youtube video... It could be for a recipe, a game review, or any other hobby or occupation.
First thing you have to do is navigate to your video of choice and click share.
Once you've clicked share, a pop-up menu will appear. Click the "Embed" option that the menu shows to you.
Once that is pressed, another menu will show (I know, I got tired of them too). You must then press the "Copy" option in order to copy the code you'll be pasting in your HTML later.
Then, you need to navigate to your html source. Depicted here in neocities.
Finally, paste the code into your source at the point you wish the video to appear.
See the example below for video help, it's slightly outdated, but the difference is mostly visual.