Edit in JSFiddle

var selected = null, // Object of the element to be moved
    x_pos = 0, y_pos = 0, // Stores x & y coordinates of the mouse pointer
    x_elem = 0, y_elem = 0; // Stores top, left values (edge) of the element

// Will be called when user starts dragging an element
function _drag_init(elem) {
    // Store the object of the element which needs to be moved
    selected = elem;
    x_elem = x_pos - selected.offsetLeft;
    y_elem = y_pos - selected.offsetTop;
}

// Will be called when user dragging an element
function _move_elem(e) {
    x_pos = document.all ? window.event.clientX : e.pageX;
    y_pos = document.all ? window.event.clientY : e.pageY;
    if (selected !== null) {
        selected.style.left = (x_pos - x_elem) + 'px';
        selected.style.top = (y_pos - y_elem) + 'px';
    }
}

// Destroy the object when we are done
function _destroy() {
    selected = null;
}

// Bind the functions...
document.getElementById('draggable-element').onmousedown = function () {
    _drag_init(this);
    return false;
};

document.onmousemove = _move_elem;
document.onmouseup = _destroy;

<div id="draggable-element">Drag me!</div>

body {padding:10px}

#draggable-element {
  width:100px;
  height:100px;
  background-color:#666;
  color:white;
  padding:10px 12px;
  cursor:move;
  position:relative; /* important (all position that's not `static`) */
}