I just built you a quick example of how to do it with jQuery: http://jsfiddle.net/gCqJ4/ It's not too hard and you can build off of my example. License is MIT.
There is a fundamental assumption being made here. First, your image is expected to already have been uploaded; this is just the crop part. Second, the image has a data-id attribute which specified the id of the image that the server can use.
I'll explain the JS a bit below:
First part is your typical jQuery plugin declaration:
(function($) {
    $.fn.croppable = function(settings) {
Then we take an optional argument of settings, with some sane defaults (success being your anonymous function for handling successful data submissions):
        settings = settings || {
            square: 50,
            default: 'middle',
            id: $(this).data("id"),
            success: null
        };
Next is just basic initial position calculation.
        var position = {
            x: settings.default == 'middle' ? ($(this).width() / 2) - (settings.square / 2) : 0 ,
            y: settings.default == 'middle' ? ($(this).height() / 2) - (settings.square / 2) : 0
        };
We wrap the image in a container that can be styled and used as the parent containment for the draggable cropper.
        $(this).wrap("<div class='croppable-container' style='position: relative;' />");
This is (obviously) the cropper.
        var cropper = $("<div style='position: absolute; top: " + position.y + "px; left: " + position.x + "px; height: " + settings.square + "px; width: " + settings.square + "px;' class='cropper' />");
Place it before the image:
        $(this).before(cropper);
Create a basic save button:
        var save = $("<input type='button' value='Crop Selection'/>");
And bind it to a service to receive posts for the cropping:
        save.click(function () {
           $.post("/your/service/location",
                  {
                      img: id,
                      x: cropper.position().left,
                      y: cropper.position().top,
                      height: settings.square
                  },
                  function (data) {
                      if (settings.success != null) {
                          settings.success(data);
                      }
                  }
            );
        });
        $(this).parent().width($(this).width());
        $(this).parent().height($(this).height());
        cropper.draggable({containment: "parent"});
        $(this).parent().after(save);
End of the typical plugin declaration:
    };
})(jQuery);
Call it:
$(".croppable").croppable();
As a final note, the plugin itself is only 1.61 KB. Small enough?