Use this to add fluidvids to your theme for responsive videos (https://github.com/toddmotto/fluidvids)

fluidvids.js

/*
  Fluid and Responsive YouTube/Vimeo Videos v1.0.0
  by Todd Motto: http://www.toddmotto.com
  Latest version: https://github.com/toddmotto/fluidvids
  
  Copyright 2013 Todd Motto
  Licensed under the MIT license
  http://www.opensource.org/licenses/mit-license.php

  A raw JavaScript alternative to FitVids.js, fluid width video embeds
*/ 
(function() {
    var iframes = document.getElementsByTagName('iframe');

    for (var i = 0; i < iframes.length; ++i) {
        var iframe = iframes[i];
        var players = /www.youtube.com|player.vimeo.com/;
        if(iframe.src.search(players) !== -1) {
            var videoRatio = (iframe.height / iframe.width) * 100;

            iframe.style.position = 'absolute';
            iframe.style.top = '0';
            iframe.style.left = '0';
            iframe.width = '100%';
            iframe.height = '100%';

            var div = document.createElement('div');
            div.className = 'video-wrap';
            div.style.width = '100%';
            div.style.position = 'relative';
            div.style.paddingTop = videoRatio + '%';

            var parentNode = iframe.parentNode;
            parentNode.insertBefore(div, iframe);
            div.appendChild(iframe);
        }
    }
})();

functions.php

<?php

//* Do NOT include the opening PHP tag. This code needs to be added to your functions.php file.

//* Add fluidvids to theme
add_action ( 'wp_enqueue_scripts', 'rgc_fluidvid' );
function rgc_fluidvid() {
	wp_enqueue_script( 'fluidvids', get_stylesheet_directory_uri() . '/lib/js/fluidvids.js', array(), false, true ); // Responsive Videos
}

//* You will need to create folders called lib/js inside your theme and put the fluidvids.js file in it, or else change the path above.