1. Log in to your authorize.net account.
   Login: *****
   PW: *****
    
2. Under Transaction Search in the left-side navigation, click Search by Business Day.
    
3. By default, the date range is the last 30 days. If the transaction took place within the last 30 days, you do not have to change any settings. Click the Search button at the bottom. This will produce all transactions for the last 30 days.
    
4. Click on the Trans ID number of the order you wish to refund. A window will appear with the order's info.
    
5. Click the Refund button at the top of the window.
    
6. By default, the total amount that you charged the customer will appear in the editable area. You can edit that amount to issue a partial refund, or not change anything to give a full refund. Click Ok to submit the refund request.

What is the difference between a refund and a void?

A void takes place before the transaction settles on the same day it was made. Voiding a transaction is preferable to issuing a refund because a settled transaction will cost you money to refund. On a refund, you will lose the amount you paid to settle it, and you may pay a fee to refund it. 
 

Therefore, if you may cancel or refund an order, try to void it on the same day as the purchase was made before it settles (this is usually by approximately 5:30 pm EST).
 

If a purchase is made after 6:30 pm EST, you have until approximately 5:30 pm the next day to void it before it settles.

...........

Here is an article about refunding a purchase on the same day it was made:

https://www.shoplocal.org/help-center.cfm/4/delete-an-order-authorizenet-on-same-day-it-was-placed