To change the whole site layout, you would use
Widget Context to hide/show widgets, as with any other part of the site.
As for the actual content output, that is all processed through the content.php file in the theme folder. You're actually the first person to ask for a way to change that specific part of the site, so unfortunately there's currently no easy way to do it without code edits.
I've added a note to my list of features to add to the framework, but I can't give any kind of time frame, as my other job is eating up most of my time at the moment.
