You can mark a task as done from the right side-panel or from the full task list.
In the right side-panel, select the Tasks icon, select the task, then select Mark done in the View task dialog.
To open the full task list, select the Tasks icon, then select the See all tasks icon at the top of the panel. On the task row, select the checkmark button. The checkmark button appears only on tasks assigned to you.
The task's Status changes to Done.
Tasks assigned to another user have no checkmark button. To mark one as done, select the pen button on the task row, change Status to Done in the Update task dialog, then select Save.