If you are not already on the Tasks Screen, navigate to it by clicking on the blue Tasks navigation button. Tasks can be marked complete and archived for either the Tasks I Assigned or the Requested Tasks sub-tab.
Marking a Task Complete:
Marking a task complete will shift it from the Current Tasks to the Completed Tasks list.
Archiving a Task:
Archiving a task will remove it from the completed list and no longer show it anywhere in the system.