User can log and submit his/her time on the scheduled tasks. Resource manager can also log time and submit on behalf of other members

To log time, go to tab TimesheetTimelog 

If you have scheduled tasks in the period just simply enter the time and click log to log your time.

You can also log time for task which is not scheduled by clicking on the white space, a dialog will show up so you can log working time time or time off

Choose task from the dropdown box or click on + button to create a new task.

Move to Time off tab to log time off

You can also track time for a specific task in Jira issue detail page