This plugin works at the order level. So, you will find the Delivery Date Field on the Checkout page of your store. There are multiple options available under General Settings > Appearance section to change the placement of the Delivery Date Field on the checkout page - 

Also, you can allow your customers for selecting delivery date on the Cart Page too by enabling the 'Delivery Date field on Cart page' option present at Order Delivery Date >> Settings >> General Settings >> Appearance tab.