Go to YouTube and select a video you wish to embed into your website. It can be your own video or someone else's.

I selected one of my videos on how to create a Facebook Business page:

Click on the Share Link as shown below:

Click on embed as shown below:

To embed the video, you would copy and paste that code into your website.

Now, let's say you want to change the size, or disallow suggested videos when the video finishes. You may not want other videos to be played following your video so to keep people on your website and avoid competition.

To do that, you would select the SHOW MORE option below the embed code and before the comments as shown here:

The Options

You will see the following options:

• You can click on the drop-down menu to select a video size that would be appropriate for your post. You have the following choices:
  
  • 420 x 315 (default)
  • 480 by 360
  • 640 x 480
  • 960 x 720
  • Custom Size
• You can deselect the "Show suggested videos when the video finishes" so to keep visitors on your website and like I said, avoid possible competition.
• Player controls are the pause, stop, etc. buttons which I think you should keep so to give your visitors options on what they want to do while viewing your video. Perhaps you are doing a video tutorial, and you want your users to be able to pause your video so they can try to do what you showed them in the video.
• You can show the video title and play actions which is good to have.
• You enable the privacy-enhanced mode. If deselected, YouTube won’t store information about visitors on your website unless they play the video.