I really recommend using some sort of library, but you asked for it, you get it:

var p = document.querySelector('p'); // element to make resizable



p.addEventListener('click', function init() {

    p.removeEventListener('click', init, false);

    p.className = p.className + ' resizable';

    var resizer = document.createElement('div');

    resizer.className = 'resizer';

    p.appendChild(resizer);

    resizer.addEventListener('mousedown', initDrag, false);

}, false);



var startX, startY, startWidth, startHeight;



function initDrag(e) {

   startX = e.clientX;

   startY = e.clientY;

   startWidth = parseInt(document.defaultView.getComputedStyle(p).width, 10);

   startHeight = parseInt(document.defaultView.getComputedStyle(p).height, 10);

   document.documentElement.addEventListener('mousemove', doDrag, false);

   document.documentElement.addEventListener('mouseup', stopDrag, false);

}



function doDrag(e) {

   p.style.width = (startWidth + e.clientX - startX) + 'px';

   p.style.height = (startHeight + e.clientY - startY) + 'px';

}



function stopDrag(e) {

    document.documentElement.removeEventListener('mousemove', doDrag, false);

    document.documentElement.removeEventListener('mouseup', stopDrag, false);

}

Demo

Remember that this may not run in all browsers (tested only in Firefox, definitely not working in IE <9).