Underneath your video on YouTube, you should see a “share” tab. Click on “embed”. It will give you a chunk of code. You don’t need to understand that code in any way…just copy it.
Go to your blog post you are working on in WordPress. You will see two little tabs on the upper-right side of the text box where you are typing. It will default to “visual” but click on “text.” Simply paste that embed text anywhere you want it, and boom, this should work. You can hit “preview” to see if it worked right before you actually publish the post.