It’s so easy it’s ridiculous. Simply surround your embed with a containing div that we can style the YouTube video responsively.

Then we add a dash of css.

.video-container {
    position: relative;
    padding-bottom: 56.25%;
    padding-top: 30px; height: 0; overflow: hidden;
}
 
.video-container iframe,
.video-container object,
.video-container embed {
    position: absolute;
    top: 0;
    left: 0;
    width: 100%;
    height: 100%;
}