You can explore two options:
1. Use this plugin – https://wordpress.org/plugins/responsive-video-embeds/
2. Or use CSS implementation. Add following code to style.css file
.videoWrapper {
position: relative;
padding-bottom: 56.25%; /* 16:9 */
padding-top: 25px;
height: 0;
}
.videoWrapper iframe {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
}and then embed video using this code format
<div class="videoWrapper">
<!-- Copy & Pasted from YouTube -->
<iframe width="560" height="349" src="http://www.youtube.com/embed/n_dZNLr2cME?rel=0&hd=1" frameborder="0" allowfullscreen></iframe>
</div>Source – https://css-tricks.com/NetMag/FluidWidthVideo/Article-FluidWidthVideo.php
P.S. Plugin method is recommended as it is automatic.