To find any orders that are pending payment, go to the orders search list and select the "Pending Payment" status from the list of statuses. Remove any other statuses from the list.
Once you find the order that you want to update, click the order number to view it's details.
If the order is pending payment, and you are not the purchaser, you will see a button to mark the order as paid.
Click that button and you can select to change the status paid, set the payment method (i.e. check, cash, etc), and provide additional details on the payment, such as the check number.
Submitting the form will update the order and send a new receipt noting that the order had been paid.