If you want to create a basic style plugin which applies styling to items placed using Panopoly, you will first need to create a custom module and set it up to use Panel's hooks. Afterwards, you create a plugin file located inside your module directory at plugins/styles/style_name.inc that looks like this:

<?php
$plugin = array(
  'title' => t('A Dark Blue Background'),
  'description' => t('Wraps panes in the Drupal dark blue style.'),
  'render pane' => 'panopoly_example_dark_blue_background_render_pane',
  'weight' => -10,
);
function theme_panopoly_example_dark_blue_background_render_pane($vars) {
  $content = $vars['content'];
  $pane = $vars['pane'];
  $display = $vars['display'];
  $plugin = $vars['style'];
  $content->css_class .= ' pane-dark-blue-background';
  return theme('panels_pane', array('content' => $content, 'pane' => $pane, 'display' => $display));
}

And a little bit of CSS:

.pane-dark-blue-background {
  background-color: #0678be;
  padding: 1em;
}