http://docs.joomla.org/Adding_a_multiple_item_select_list_parameter_type

Thats the documentation for the best way to give a custom parameter type for your module and when you consider the bottom round there's this line : Saving parameter values to some database

Please can someone let me know if there's any documentation regarding how to do that in Joomla 1.6 because I am unable to think it is anywhere?

I realize completely the salt water evaporates though, You have to bind your custom options (example: their email list selection from the multiple selection input box) towards the parent to ensure that it'll have the ability to save the choice towards the DB.

Thanks ahead of time.

EDIT added code

protected function getInput()
    {

        $options = array();
        $attr = '';

        $attr .= ' multiple="multiple"';
        $attr .= ' style="width:220px;height:160px;"';

        // Get the database instance
        $db = JFactory::getDbo();
        // Build the select query
        $query = 'SELECT params FROM jos_modules'
            . ' WHERE module="mod_pmailer_subscription"';
        $db->setQuery($query);
        $params = $db->loadObjectList();

        // Decode the options to get thje api key and url
        $options = json_decode($params[0]->params, true);

        // Create a new API utility class
        $api = new PMailerSubscriptionApiV1_0(
            $options['enterprise_url'],
            $options['pmailer_api_key']
        );

        // Get the lists needed for subscription
        $response = $api->getLists();

        // Make a default entry for the dropdown
        $lists = array('0' => 'Please select a list');

        // Builds the options for the dropdown
        foreach ( $response['data'] as $list )
        {
            $lists[$list['list_id']]['id']    = $list['list_id'];
            $lists[$list['list_id']]['title'] = $list['list_name'];
        }

        // The dropdown output
        return JHTML::_(
            'select.genericlist',
            $lists,
            'jform[params][list_id]',
            trim($attr),
            'id',
            'title',
            $options['list_id']
        );

    }

Checkout this, How you can convert JParams to JForm

EDIT :

I checked the forum and located that you're using

// Builds the options for the dropdown
foreach ( $response['data'] as $list )
{
   $lists[$list['list_id']] = $list['list_name'];
}

however in JHTML you're passing id and title for text and cost area,

Use

    // Builds the options for the dropdown
    foreach ( $response['data'] as $list )
    {
        $lists[$list['list_id']]['id']    = $list['list_id'];
        $lists[$list['list_id']]['title'] = $list['list_name'];
    }