The easy way:
first, get your element with e.g. getElementById, then set innerHTML to your new code.
var div = document.getElementById('special-id');
div.innerHTML = '<span>hello world</span>';
The DOM method only way:
create your new HTML nodes using document.createElement or document.createTextNode
and then append them to your element with appendChild.
// assuming `div` as above
var newNode = document.createElement('span');
span.appendChild(
document.createTextNode('hello world')
);
div.appendChild(span);