Due Dates are listed on the task tiles on your project and on the task dialog.
Overdue tasks are marked yellow until they are completed to put your focus on them.
To set a due date for a task simply open the task and click on "Due Date" on the right side of the task dialog. A calendar will show up allowing you to choose the due date. The due time will be automatically set to 12PM unless you change it.
Tasks will show up in the "My Tasks" menu on the day they are due and will stay there until completed when they are overdue.