If the custom field contains only the video URL, for example http://www.youtube.com/watch?v=dQw4w9WgXcQ, you can get the oEmbed HTML code with wp_oembed_get :
$videourl = 'http://www.youtube.com/watch?v=dQw4w9WgXcQ';
$htmlcode = wp_oembed_get($videourl);
echo $htmlcode;
, URL-, the_content the_content:
$content = "<h2>this video is great</h2>\n<p>check it out</p>\n"
. "[embed]http://www.youtube.com/watch?v=dQw4w9WgXcQ[/embed]";
$htmlcode = apply_filters('the_content', $content);
echo $htmlcode;