Go to your inspection grid by clicking on Inspections and then selecting View Inspections. Choose your desired inspection and click on Actions -> Payment Information.
Click on the appropriate payment type (add cash, check, money order payment, etc.), enter the inspection fee collected, enter the check number if applicable and click on add payment. In order to run credit cards through the ISN you must set this up with your credit card vendor. (to enable it in your ISN click on Settings, Office Settings and then Payment Options)
After you have added a payment to an inspection the paid icon on your inspection grid will automatically change to a green square with white checkmark on the inspection grid.