When your ZenCart store receives an order, you as store administrator should receive one email from ZenCart indicating the order.  And depending on your payment module, you may also get another email from your payment processor saying that you have received money.  If you are using PayPal Website Payment Standard, PayPal sends you an email notification saying you've received money.

In the Zencart order notification email, it indicates to you the items and the shipping address.  Alternatively, you can see that information in the ZenCart administrative control panel under "Customers -> Orders".  

You can see that the orders that needs to be fulfill are marked as "Processing". 

In our example, you see that there is a red dot next to this particular
order. This is just a warning to indicate that the shipping and billing
address for this order did not match. Some merchants like to examine
such order more carefully. However, since it is perfectly fine for the
two addresses to be different, this is not an error. The transaction
goes through successfully just as normal.

If order has yellow square ...

that means that customer had placed a comment during the order process.

To see the details of the order with a line-item breakdown, click the invoice
button. It will also show the customer contact information, billing
address, shipping address, ship method, payment method, and the customer comments. This is all
the information that you need to fulfill the order.

Next, you have to ship those items to your customer.  As merchant, you may want to include an packing slip in the package. If so, click the Packing Slip button and print it out.

Once you have shipped the package via the specified shipping method,
you can notify the customer that the order has been shipped by clicking
the Edit button...

Scroll to the bottom of the page and change the status to Delivered and click Update. See below picture.

 

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