You can use the Survey module to view OOTB surveys which you can copy and adapt, or create a new Survey via Survey designer. Make sure that Send Notifications is True:

After setting up the survey, you can use the Trigger Conditions related list to set up a new condition e.g:

Table = Incident; User field (i.e. send to) = Caller; Condition = Incident changes to Closed. 

The reference fields stores the associated values with the survey record to help with reporting. More on that here

Hope this helps!