POSTing form/showing results within div

Say I have a div with a form in it. What I would like to do is POST
the form to a php script, then show the results that the php page
outputs in that same div, without refreshing the entire page.

This seems like a client side issue, so, I would think it could be
done in Javascript, however, I'm not sure how. I downloaded the
Javascript Prototype library, so if there is a way to do it with that
library, then that would be good.

Does any one know how to do this or have suggestions?

Thanks.