Add preprocess entity to module so that variables can be sent to custom templates

I think Entity API provides those preprocess functions for us, no?

Like hook_preprocess_entity() and I think even hook_preprocess_group?

Right, what you need is hook_preprocess_entity(). Then check if $variables['entity_type'] == 'group'

is any way someone can post a code example of how this would be implemented, Im a designer trying to style a theme for the group module and I cant figure out how to get $group variables into the templates? Cant seem to find a code example anywhere. ive searched hi and lo. Specifically, i want to render an image field from the group in the page--group.tpl.php but outside of the content, just above the title. I can access the variable in the devel module and target the field that way, but then the id of the group is passed and so will only load 1 groups image, but the goal is to load a header image for each group that is unique to the group and comes from a field of the group, ie an image field.

I know it's probably really easy for someone, but for me this is nearly impossible to figure out. Any help would be greatly appreciated!

Look at template_preprocess_entity()

/**
 * Process variables for entity.tpl.php.
 */
function template_preprocess_entity(&$variables) {
  $variables['view_mode'] = $variables['elements']['#view_mode'];
  $entity_type = $variables['elements']['#entity_type'];
  $variables['entity_type'] = $entity_type;
  $entity = $variables['elements']['#entity'];
  // THIS LINE ALREADY SETS A $group VARIABLE
  $variables[$variables['elements']['#entity_type']] = $entity;

  // Snip

  // THESE LINES ADD group.tpl.php, group--type.tpl.php, ETC. AS SUGGESTIONS
  // Add suggestions.
  $variables['theme_hook_suggestions'][] = $entity_type;
  $variables['theme_hook_suggestions'][] = $entity_type . '__' . $bundle;
  $variables['theme_hook_suggestions'][] = $entity_type . '__' . $bundle . '__' . $variables['view_mode'];
  if ($id = entity_id($entity_type, $entity)) {
    $variables['theme_hook_suggestions'][] = $entity_type . '__' . $id;
  }
}

It should work out of the box

Thanks for the example Kristiaan!
I added the code you provided above to my custom module and it seems to be creating the template suggestions but my snippet of code I usually use for inserting fields(on page.tpl.php templates) from nodes is not working. How can I alter this code to target the group entity type since the node variable is not available? my field is "field_header_image". thanks again.

    $field = field_view_field('node', $node, 'field_header_image', array('label'=>'hidden'));
     print render($field);
    

You shouldn't copy any of the code above (#7), Entity API runs that for you for any custom entity type (group, commerce product, ...).

What I was saying is that you should have a $group variable in group.tpl.php out of the box, just as you should have a $node variable in node.tpl.php out of the box because the node module takes care of that in template_preprocess_node().

Maybe you're getting confused by the theming layer a little bit :) This link has some documentation on preprocessors: https://www.drupal.org/node/223430

P.S.: Even though you shouldn't call field_view_field() in a template, it would look like this:

$field = field_view_field('group', $group, 'field_X', $options);

cool thanks