How to append data to div using JavaScript?

Try this:

var div = document.getElementById('divID');

div.innerHTML += 'Extra stuff';

Using appendChild:

var theDiv = document.getElementById("<ID_OF_THE_DIV>");
var content = document.createTextNode("<YOUR_CONTENT>");
theDiv.appendChild(content);

Using innerHTML:
This approach will remove all the listeners to the existing elements as mentioned by @BiAiB. So use caution if you are planning to use this version.

var theDiv = document.getElementById("<ID_OF_THE_DIV>");
theDiv.innerHTML += "<YOUR_CONTENT>"; 

Beware of innerHTML, you sort of lose something when you use it:

theDiv.innerHTML += 'content';

Is equivalent to:

theDiv.innerHTML = theDiv.innerHTML + 'content';

Which will destroy all nodes inside your div and recreate new ones. All references and listeners to elements inside it will be lost.

If you need to keep them (when you have attached a click handler, for example), you have to append the new contents with the DOM functions(appendChild,insertAfter,insertBefore):

var newNode = document.createElement('div');
newNode.innerHTML = data;
theDiv.appendChild(newNode);