If you are concerned about web site performance, you probably noticed that embedded YouTube iframes are costly. Instead of iframes, you may embed images that link to the respective videos, and make these links replace themselves with iframes when clicked. (IE 9+ because of getElementsByClassName.)

yt-embed.js

/*jshint maxlen: 79 */

var MYSITE = {};

/**
 * Make YouTube links with .yt-embed replace themselves with YouTube
 * iframes when clicked; firstElementChild is assumed to be the
 * img element holding the poster frame; the YouTube URL must contain
 * the "v" parameter and no further parameters.
 *
 * @param {Document} d The window.document object.
 */
MYSITE.yt_embed = function (d) {
    'use strict';

    var el,
        els = d.getElementsByClassName('yt-embed'),
        i,
        max;

    var replace_with_iframe = function (event) {
        var iframe = d.createElement('iframe'),
            video_id = event.currentTarget.href.split('=')[1];

        iframe.width = event.currentTarget.firstElementChild.width;
        iframe.height = event.currentTarget.firstElementChild.height;
        iframe.setAttribute('allowfullscreen', true);
        iframe.src = 'https://www.youtube-nocookie.com/embed/' +
            video_id +
            '?autoplay=true';

        event.currentTarget.parentElement.replaceChild(
            iframe, event.currentTarget
        );

        event.preventDefault();
    };

    for (i = 0, max = els.length; i < max; i++) {
        el = els[i];
        el.addEventListener("click", replace_with_iframe);
    }
};

yt-embed.min.js

var MYSITE={yt_embed:function(d){"use strict";var e,f=d.getElementsByClassName("yt-embed"),a,g,h=function(b){var c=d.createElement("iframe"),a=b.currentTarget.href.split("=")[1];c.width=b.currentTarget.firstElementChild.width;c.height=b.currentTarget.firstElementChild.height;c.setAttribute("allowfullscreen",!0);c.src="https://www.youtube-nocookie.com/embed/"+a+"?autoplay=true";b.currentTarget.parentElement.replaceChild(c,b.currentTarget);b.preventDefault()};a=0;for(g=f.length;a<g;a++)e=f[a],e.addEventListener("click",h)}};

yt-example.html

<style>
iframe { border: 0; }
</style>

<a href="https://www.youtube.com/watch?v=VIDEOID" class=yt-embed>
    <img src=poster.jpg alt="YouTube video" width=320 height=180>
</a>

<script src=yt-embed.min.js></script>
<script>
MYSITE.yt_embed(window.document);
</script>