Really depends on the overall structure of your document.
If you have:
<div></div>
<div></div>
<div></div>
it may be as simple as traversing through using
mydiv.nextSibling;
mydiv.previousSibling;
However, if the 'next' div could be anywhere in the document you'll need a more complex solution. You could try something using
document.getElementsByTagName("div");
and running through these to get where you want somehow.
If you are doing lots of complex DOM traversing such as this I would recommend looking into a library such as jQuery.