There are two different function fields depending on what module you are wanting to use it with. From what I can see the first one is for the newer modules e.g contacts,account etc

$dictionary["Contact"]["fields"]['account_country_c'] =
    array (
        'name' => 'account_country_c',
        'vname' => 'LBL_ACCOUNT_COUNTRY_C',
        'type' => 'function',
        'source' => 'non-db',
        'studio' => 'visible',
        'function' =>
            array (
                'name' => 'account_country_function',
                'returns' => 'html',
                'include' => 'custom/modules/Contacts/customfields.php'
            ),
    );

the file it relates to contains 

function account_country_function($focus, $field, $value, $view){

    $bean = BeanFactory::getBean("Accounts", $focus->account_id);



    return $bean->shipping_address_country;

}

The following is for what looks like the older modules for example Campaigns.

$dictionary['CampaignLog']['fields']['account_country2_c'] =    array (

        'name' => 'account_country2_c',
        'type'=>'function',

        'reportable'=>false,

        'source'=>'function',

        'function_name'=>'account_country_function',

        'function_class'=>'custom_contact_fields',

        'function_require'=>'custom/modules/Contacts/customfields.php',

        'function_params'=> array('account_id'),

        'function_params_source'=>'this',  //valid values are 'parent' or 'this' default is parent.
    );

class custom_contact_fields{

function account_country_function($account_id){

$bean = BeanFactory::getBean("Accounts", $account_id);



return $bean->shipping_address_country;

}

}