<script type="text/javascript">
	// $('#YTembed') is the ID of your input field
	$('#YTembed').change(function(){
		var txt = $(this).val(); // get the value that the user supplied
		var flag = false; // Use this flag variable to discern between good and bad entry > Assumes good
		// First try the normal youtube URL:
		var arr = txt.split('v=');
		if (arr.length > 1){
			// normal Youtube URL detected
			var vidcode = arr[1].substr(0,11); // Substring get the 11 characters
		} else if (txt.indexOf('youtu.be') > -1) {
			// Normal URL check failed > try the shortened one
			arr = txt.split('youtu.be'); // Split on shortened URL
			var vidcode = arr[1].substr(1,11); // Grab the 11 characters from the slash onward
		} else {
			// No result > Flag for output
			flag = true;
		}

		if (!flag) $('#vidfeedback').html('<iframe width="580" height="326" src="http://www.youtube.com/embed/'+vidcode+'" frameborder="0" allowfullscreen></iframe>');
		else $('#vidfeedback').html("That doesn't appear to be a Youtube URL. Please try again.<br/>We accept the following formats:<br/>http://www.youtube.com/watch?v=XXXXXXXXXXX or <br/>http://youtu.be/XXXXXXXXXXX");
	});
</script>

<script type="text/javascript">
	// $('#YTembed') is the ID of your input field
	$('#YTembed').change(function(){
		var txt = $(this).val(); // get the value that the user supplied
		var flag = false; // Use this flag variable to discern between good and bad entry > Assumes good
		// First try the normal youtube URL:
		var arr = txt.split('v=');
		if (arr.length > 1){
			// normal Youtube URL detected
			var vidcode = arr[1].substr(0,11); // Substring get the 11 characters
		} else if (txt.indexOf('youtu.be') > -1) {
			// Normal URL check failerd > try the shortened one
			arr = txt.split('youtu.be'); // Split on shortened URL
			var vidcode = arr[1].substr(1,11); // Grab the 11 characters from the slash onward
		} else {
			// No result > Flag for output
			flag = true;
		}

		if (!flag) $('#vidfeedback').html('<iframe width="580" height="326" src="http://www.youtube.com/embed/'+vidcode+'" frameborder="0" allowfullscreen></iframe>');
		else $('#vidfeedback').html("That doesn't appear to be a Youtube URL. Please try again.<br/>We accept the following formats:<br/>http://www.youtube.com/watch?v=XXXXXXXXXXX or <br/>http://youtu.be/XXXXXXXXXXX");
	});
</script>

<script type="text/javascript">
	$('#YTembed').change(function(){
		var txt = $(this).val(); // get the value that the user supplied
		var flag = false; // Use this flag variable to discern between good and bad entry > Assumes good
		// First try the normal youtube URL:
		var arr = txt.split('v=');
		if (arr.length > 1){
			// normal Youtube URL detected
			var vidcode = arr[1].substr(0,11); // Substring get the 11 characters
		} else if (txt.indexOf('youtu.be') > -1) {
			// Normal URL check failerd > try the shortened one
			arr = txt.split('youtu.be'); // Split on shortened URL
			var vidcode = arr[1].substr(1,11); // Grab the 11 characters from the slash onward
		} else {
			// No result > Flag for output
			flag = true;
		}

		if (!flag) $('#vidfeedback').html('<iframe width="580" height="326" src="http://www.youtube.com/embed/'+vidcode+'" frameborder="0" allowfullscreen></iframe>');
		else $('#vidfeedback').html("That doesn't appear to be a Youtube URL. Please try again.<br/>We accept the following formats:<br/>http://www.youtube.com/watch?v=XXXXXXXXXXX or <br/>http://youtu.be/XXXXXXXXXXX");
	});
</script>

Use this snippet to check if user supplied URL is a valid Youtube URL. Has support for youtu.be shortened URL's too.

Get the Youtube ID from a Youtube URL (Shortened URL support too)

url

jQuery