The per diem clock starts at report time for a trip and ends at release time for that trip. So if my report time is 10am on the 14th and release is 4pm on the 17th it would look like this:

14hrs on the 14th
24hrs on the 15th
24hrs on the 16th
16hrs on the 17th

For a total of 78hrs of per diem. That money is tax free and shows up on one of your pay checks, depending on how your company's payroll works.