By default all the orders are saved to the database. You can disable this feature in Products > Settings > Shopping Cart in the Orders section. Check the checkbox to disable order registration:
All the orders are shown in admin orders menu.
You can click the order to see all the details.
Customer Details Section
The Customer Details section shows all the checkout fields filled. In the example there are only two fields in the checkout.
You can change all the customer details fields values.
Order Data Section
In the order data column you can edit the payment status. Set it to Pending or Completed.