Using Order Delivery Date v2.6.1 and OPC v2.0.4 on Zen Cart 1.5.5f. Here's what's needed for the integration:

* Update your template's version of checkout_one.css, appending the styling provided by ODD's checkout_shipping.css.

* Copy the ODD files provided in /includes/modules/pages/checkout_shipping to /includes/modules/pages/checkout_one.

* Copy /includes/templates/template_default/templates/tpl_modules_opc_shipping_choices.php to /includes/templates/YOUR_TEMPLATE/templates/ and make the changes highlighted below:
Code:
    <div id="checkoutShippingContentChoose" class="important"><?php echo TEXT_NO_SHIPPING_AVAILABLE; ?></div>
<?php
    }
?>
<!-- Bof Order Delivery Date -->
<?php if (isset($display_delivery_date) ? $display_delivery_date : true) { ?>
<fieldset class="shipping" id="order_delivery_date">
<legend><?php echo sprintf(TABLE_HEADING_DELIVERY_DATE, (defined('MIN_DISPLAY_DELIVERY_DATE') && MIN_DISPLAY_DELIVERY_DATE > 0 && (method_exists($zcObserverOrderDeliveryDateObserver, 'display_delivery_date') ? $zcObserverOrderDeliveryDateObserver->display_delivery_date($order) : true)) ? TABLE_HEADING_DELIVERY_DATE_IS_REQUIRED : TABLE_HEADING_DELIVERY_DATE_IS_OPTIONAL); ?></legend>

<label for="order_delivery_date">Date:</label>
<input id="date" name="order_delivery_date" type="text" value="<?php echo $order_delivery_date; ?>">
</fieldset>
<?php } ?>
<!-- Eof Order Delivery Date -->
<?php
}  //-Order is not "virtual", display full shipping-method block
* Copy /includes/templates/template_default/templates/tpl_checkout_one_confirmation.php to /includes/templates/YOUR_TEMPLATE/templates/ and make the changes highlighted below:
Code:
        <h3 id="checkoutConfirmDefaultShipment"><?php echo HEADING_SHIPPING_METHOD; ?></h3>
        <h4 id="checkoutConfirmDefaultShipmentTitle"><?php echo $order->info['shipping_method']; ?></h4>
<?php
 /* BEGIN Order Delivery Date */
  if (isset($display_order_delivery_date) && $display_order_delivery_date) { ?>
  <br />
  <h3><?php echo TABLE_HEADING_DELIVERY_DATE; ?></h3>
  <div class="buttonRow forward"><?php echo '<a href="' . $editShippingButtonLink . '">' . zen_image_button(BUTTON_IMAGE_EDIT_SMALL, BUTTON_EDIT_SMALL_ALT) . '</a>'; ?></div>
  <h4><?php echo $order_delivery_date_text; ?></h4><br />
<?php } /* END Order Delivery Date*/ 
        }
?>
    </div>
* Update your admin's Configuration->One-Page Checkout Settings, adding each payment method you support to the Payment Methods Requiring Confirmation list.

* Copy /includes/languages/english/checkout_one_confirmation.php to /includes/languages/english/YOUR_TEMPLATE/checkout_one_confirmation.php and add the language constants required by ODD (you wouldn't need to do this if they were in an extra_definitions file).