How to add field for new site-wide option on Network Settings screen?

There’s a wpmu_options action that lets you append more HTML on the Network Settings page.

If you want to add your own sub-menu/page to the Settings parent menu:

add_action('network_admin_menu', 'add_my_netw_settings_page');
function add_my_netw_settings_page() {
  add_submenu_page(
       'settings.php',
       'Co za asy',
       'Co za asy',
       'manage_network_options',
       'my-netw-settings',
       'your_form'
  );    
}

function your_form(){
  $options = get_site_option('your_plugin');

  ?>
  <form action="<?php echo admin_url('admin-post.php?action=update_my_settings'); ?>" method="post">
    <?php wp_nonce_field('your_plugin_nonce'); ?>

    ...fields go here...

  </form>
  <?php
}

the save handler:

add_action('admin_post_update_my_settings',  'update_my_settings');
function update_my_settings(){     
  check_admin_referer('your_plugin_nonce');
  if(!current_user_can('manage_network_options')) wp_die('FU');

  // process your fields from $_POST here and update_site_option

  wp_redirect(admin_url('network/settings.php?page=my-netw-settings'));
  exit;  
}

Keep the save handler if you choose to use that action I mentioned above, and hook the form to that action.