I want two full columns after the header and main menu bar on my index page. Seems simple, but googling and prowling the wordpress.org site hasn't gotten me anywhere. Short explanation + a link to relevant section of TFM to R would be much appreciated.
It depends on the theme you are using. The index.php file in your theme applies to your home page. So if you change the HTML structure in there to be 3 columns, your home page should be 3 columns.
Be careful though because index.php will also apply in some cases beyond the home page. Take a look at the Template Hierarchy for the order of precedence theme files are matched on for any given request.