How to include jQuery libraries into your document you can read in this post. After you've done that in the body section you need to include this three fields (year, month, day), which will handle user input.

<label for="year">Year</label>
	<select name="year" id="year">
	<option value=""></option>
	<option value="1959">1959</option>
	...
	<option value="1986">1986</option>
	</select>
<label for="month">Month</label>
	<select name="month" id="month" disabled="disabled">
	<option value=""></option>
	<option value="1">January</option>
	...
	<option value="12">December</option>
	</select>
<label for="day">Day</label>
	<select name="day" id="day" disabled="disabled">
	<option value=""></option>
	</select>

If you don't feel like copying the drop down for each year you can user "for" loop, which will do the work for you. In our case for year drop down we will have to paste this code:

for($i=1959;$i<=1986;$i++) {
	echo "<option value=\"$i\">$i</option>";
}

We can actually do the same thing for months drop down, but in this case we will have to save all the months in an array and use "foreach" loop.

$month = array('January','February','March','April','May','June','July','August','September','October','November','December');
$i=1;
foreach($month as $months) {
	echo "<option value=\"$i\">$months</option>";
	$i++;
}

Easy, isn't it?:) Let's start to use some magic to make our example work. As you can notice I disabled month and day fields and will enable them first after we will get any input from user. Let's take a look at the code, which will enable those fields for us. Don't forget to put it in the head section of your document.

$(document).ready(function(){
	$('#year').change(function(){
		$('#month').removeAttr('disabled');
	});
});

This simple code will be executed after the DOM is loaded and will trigger the removeAttr function on our drop down with id 'month' on onchange event of id element 'year'. Let's move further and see what happens, if our user chooses a month.

$(document).ready(function(){
	$('#year').change(function(){
		$('#month').removeAttr('disabled');
	});
	$('#month').change(function(){
		var leap_year = $('#year').val();
		var leap_days = (leap_year%4 == 0) ? 29 : 28;
		$.ajax({
			data:'month='+$(this).val()+'&leap='+leap_days,
			url:'leap_helper.php',
			type:'POST',
			error:function(){
				alert('something went wrong');
			},
			success:function(r){
				$('#day').removeAttr('disabled').html(r);
			}
		});
	});
});

As you can see we trigger a function on onchange event for id element 'month'. We read the value of the year drop down and save it in as leap variable. We then use modulo operator to check, if the division by four is equal zero. If it is, we assign 29 days to variable leap_days, in other case 28. We then call AJAX function of jQuery and prepare our data string, which we will use to pass the information about the month and the amount of days in leap year to our PHP script. To send the data we will use the POST method. If our script encounters error, we will alert a message, that something went wrong. (In this place you can do, whatever you feel like. For example it would be nice, if you would display a nice error message above the date input fields.) If we will get a success response from our script we will firs remove the disable attribute from the element with id 'day' and paste a drop down with the amount of days.

Let's take a closer look at our PHP file. You need to save it in the same directory and give it a name 'leap_helper.php'. If you want to use other names or directory structure, you need to change its' name in jQuery function.

$day_30 = array(4,6,9,11);
$day_31 = array(1,3,5,7,8,10,12);
$day_28 = array(2);
$day = '';
if(in_array($_POST['month'],$day_30)) {
	for($i=1;$i<31;$i++) {
	$day .= "<option value=\"$i\">$i</option>\n";
	}
} elseif(in_array($_POST['month'],$day_31)) {
	for($i=1;$i<32;$i++) {
		$day .= "<option value=\"$i\">$i</option>\n";
	}
} elseif(in_array($_POST['month'],$day_28)) {
	for($i=1;$i<=$_POST['leap'];$i++) {
		$day .= "<option value=\"$i\">$i</option>\n";
	}
}
echo $day;

In our PHP file we save three arrays for months, with 30, 31 and 28 or 29 days and initialize our $day variable. After that we perform a simple check, if the month our user choose is in the array of months with different amount of days. If it is, then we create a string with exact amount of days for chosen month. In our last case we use additionally the leap variable to display amount of days in February according to the year chosen by the user.

I hope this short explanation will help you in developing your own application. Obviously to check, if 1644 was a leap year, it wont be enough to divide it by four. For this kind of case you need a little bit more complicated formula. For our case it's just enough, if you divide by four and pass this value to our PHP script, which will create a string for you. Have fun with this script, and as usually I'm waiting for your responses. Cheers!