Simply copy the YouTube video URL and place it on your post (do not add any formatting options to the URL; you should also jump a line before and after the video URL).
This is how it would look when editing the post:
This is what you should see once the post has been published (you will see the video, not the URL):
Assuming you have just published a post which contains an YouTube URL and the result is similar to the image bellow (you don’t see the video, only the URL):
This is not an issue with our website, the problem here is the video you are trying to use does not allow embedding.
If you want to verify if the video you want to use can be embedded: