function db_tuning_analyze() { 
  
  print_r($_POST['edit']);
  print "<br />";
  foreach ($_POST['edit'] as $stuff) {
  	print $stuff;
  	print "<br />";
  	print_r($_POST['edit']['db_tuning']);
  }
  
	$form['db_tuning']['analyze_db'] = array(
	  '#type' => 'button', 
	  '#value' => t('Analyze'));

	$form['db_tuning']['apply_changes'] = array(
	  '#type' => 'button',
	  '#value' => t('Apply Changes'));
	 
	return drupal_get_form('actions', $form);
}

/** actions is a bad name for your form, change it **/
/** Note: Only do this in submit if you aren't staying on the form. **/
function actions_submit($form_id, $form_values) {
  if ($_POST['op'] == t('Apply Changes') {
    ... apply changes ... 
  }

  if ($_POST['op'] == t('Analyze') {
     ... analyze ....
  }
}