Basic draggable example using vanilla JavaScript.

draggable-example.js

'use strict';

/**
 * Makes an element draggable.
 *
 * @param {HTMLElement} element - The element.
 */
function draggable(element) {
	var isMouseDown = false;

    // initial mouse X and Y for `mousedown`
    var mouseX;
    var mouseY;

    // element X and Y before and after move
    var elementX = 0;
    var elementY = 0;

	// mouse button down over the element
    element.addEventListener('mousedown', onMouseDown);

	/**
     * Listens to `mousedown` event.
     *
     * @param {Object} event - The event.
     */
	function onMouseDown(event) {
        mouseX = event.clientX;
        mouseY = event.clientY;
        isMouseDown = true;
    }

	// mouse button released
    element.addEventListener('mouseup', onMouseUp);

	/**
     * Listens to `mouseup` event.
     *
     * @param {Object} event - The event.
     */
	function onMouseUp(event) {
        isMouseDown = false;
        elementX = parseInt(element.style.left) || 0;
        elementY = parseInt(element.style.top) || 0;
    }

	// need to attach to the entire document
    // in order to take full width and height
    // this ensures the element keeps up with the mouse
    document.addEventListener('mousemove', onMouseMove);

	/**
     * Listens to `mousemove` event.
     *
     * @param {Object} event - The event.
     */
	function onMouseMove(event) {
    	if (!isMouseDown) return;
        var deltaX = event.clientX - mouseX;
        var deltaY = event.clientY - mouseY;
        element.style.left = elementX + deltaX + 'px';
        element.style.top = elementY + deltaY + 'px';
    }
}

index.html

<style>
    #element {
        width: 100px;
        height: 100px;
        background: skyblue;
        position: relative;
    }
</style>

<div id="element"></div>

<script src="draggable-example.js"></script>
<script>
    draggable(document.getElementById('element'));
</script>