From the service information page for the customer, choose the actions drop-down menu and select "Update account status"
In the resulting dialogue box, select the "on-hold" status from the drop down menu and hit "confirm." You will generally put a customer on hold when they still want service but aren't paying their bills.
You will generally deactivate a customer when it's understood by both parties that service will no longer continue unless requested again by the customer.
You can send messages to your on-hold or inactive customers through the Advanced Search as shown here.
You can find a report of your on-hold or inactive customers in the Delinquent Report as shown here.