Regardless of where you are looking at your task - Tasks Page, Task Board, Dashboard Widget, Contact Record, Grant, Communication - you'll find a checkbox on its right to mark it as complete.
Depending on the type of task itself, Virtuous will prompt you to leave a note (grant and communication tasks will not prompt for a note). You can choose to not leave a note by unselecting "Create a contact note for this task"
Remember that Tasks are future actions and Notes are past actions.
If you complete a task accidentally, you can always go to the task board and drag that task back to the appropriate status.