If there are currently no dates set for the task, click the hyphen (-) below the Start Date and/or Due Date and select an appropriate date from the pop-up calendar. Alternatively, if there are dates already set, click on the current date to open the pop-up calendar. To remove a date, hover over the current date until a appears which you can click to keep the specified date field blank.
Users will need view and edit permissions in tasks to perform this action. Depending on the user's project permission settings, they may be able to view all project tasks or just a subset. Watchers specifically added to the task will be able to view it.