If you go to the Youtube video, you'll see there's an option to Share. If you click on it, you'll see an option to EMBED
When you click on "embed", a pop-up window will show up with a code and some options. Here you can customize how the video will appear i.e if you want it to start at a certain point, if you want suggested videos to show up at the end, if you want to show the controls, video title, etc. You can leave as is or add your preferences.
Once you are done, you can click on the link at the end that says COPY and this will automatically copy the YouTube video code
Once you copy the code, you can go to the page on the website and edit
Once in the page, place your cursor where you want the video to show up
In the editor, click Insert and select Insert Media
Paste the embed code you got from Youtube and click ok to save
The video will be inserted on the page (you'll see a grey box)
Click Submit
Always preview your page before publishing to make sure that everything looks good