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.