I don’t think you have to install Jetpack….
As others have said, get the embed code of the YouTube video. Here is an example of one at 560×315
<iframe width="560" height="315" src="https://www.youtube.com/embed/O4THpbKZ0Zg" frameborder="0" allowfullscreen></iframe>
Let’s say you want it to be only 400 wide…. Here is how I fix the YouTube embed coding to embed videos with a width of 400px into my WP posts using object:
560 divided by 400 = 1.4
315 divided by 1.4 = 225
<table id="video"><tr><td>
<a href="https://www.youtube.com/watch?v=O4THpbKZ0Zg" title="YouTube: How To Embed A YouTube Video In WordPress">YouTube: How To Embed A YouTube Video In WordPress</a>
<object data="https://www.youtube.com/embed/O4THpbKZ0Zg" title="How To Embed A YouTube Video In WordPress" width="400" height="225" allowscriptaccess="always" allowfullscreen="true">
<param name="movie" value="https://www.youtube.com/embed/O4THpbKZ0Zg" /><param name="allowFullScreen" value="true" /><param name="allowscriptaccess" value="always" /><br />Slow load or no load? Please go directly to the <a href="https://www.youtube.com/watch?v=O4THpbKZ0Zg" title="YouTube: How To Embed A YouTube Video In WordPress">video</a></object>
</td></tr></table>
You don’t have to house the video in a table. I just like to so that I can include the link, just in case….