Adding time spent on a ticket:
To add time spent on a ticket, either click on the Add Update or Add Private Note.
Click on "Update Ticket" or "Add Private Note"
The time added during the update gets logged to the total time spent on the ticket.
You can alternately add time on a ticket by clicking the add link at the Time Spent section on a ticket.
The Total time spent on a ticket is visible at the Time Spent Section of a ticket.