How do I add a class to a section in omega?
This is untested, but I am pretty sure you just need to put this in mytheme/preprocess/preprocess-section.inc:

function mytheme_alpha_preprocess_section (&amp;$variables)
{
  $variables['attributes_array']['class'][] = 'my-custom-class';
}


If you look at section.tpl.php, just $attributes gets printed out.  alpha_process() flattens $variables['attributes_array'] into $attributes.

Though, given that the header, content, and footer sections are unique, you probably don't need to explicitly add a class.  You can also add classes to the zone and zone wrappers inside each section directy with the UI at admin/appearance/settings/mytheme, or just replace "section" with "zone" in the code above.