Get the Embed Code
After clicking the SHARE option beneath your selected video.
Click the Embed link next.
This will reveal the needed video embed code as such:
You may notice the iframe tags within the code. This is what tells WordPress to create a Frame within which to present the video.
Copy this!
Step 4: Placement in your Post or Page
Then, simply past the embed code into your post or page where you wish it to appear - using the TEXT editor mode within WordPress - as such:
And, BOOM, you're done.
I typically do this after I have completed everything else within my post or page. I typically use the Visual mode of the post/page editor and with the video embed code in there already, I feel it slows me down. So, I save video and image insertions as my last step. This is a personal preference thing, of course.
Okay, the next couple of pages of this post is a wee trick I personally use to help me find the location of where I want the video. This wee trick is very helpful when you have a longer format for your posts. Having a post or page that is in excess of 1500 words can make it fun finding that specific spot for insertion when you switch to the TEXT editor instead of the visual editor.