Adding Sub-Tasks is very similar to adding Tasks. In any list of Tasks, locate the Task to which you wish to add Sub-Tasks. In the second column from the right of the Task List, you will see a drop down arrow which, if clicked, will expand that Task's Sub-Tasks. At the bottom of the list of Sub-Tasks is an empty row allowing you to add a new Sub-Task. If there are no Sub-Tasks, then a plus (+) symbol lets you add the first Sub-Task to that parent Task.
When adding Sub-Tasks in-line, as in the above image, you cannot alter the Project or Department context, as these will always be the same as that of the parent Task.
You can also add a Sub-Task from within the Task Details Page of the parent Task to which it relates. Click on that Task and then in the Task Details screen click on the "Sub-Tasks" tab where you will see a plus (+) button allowing you to add new. Fill in the form as you would to enter a new Task and, once you have completed the form, your new Sub-Task will be logged in the system with that Task as its parent.