You can add this to your functions.php file –
//* Remove the entry meta in the entry footer (requires HTML5 theme support)
remove_action( 'genesis_entry_footer', 'genesis_post_meta' );
This comes from the Genesis Framework documentation which is all covered here – http://my.studiopress.com/snippets/entry-footer/#remove-entry-meta in the Code Snippets section.
There are many more tutorials and code snippets on StudioPress which can be found here – http://my.studiopress.com/