Use rarely, and only to indicate the intentional omission of words in a quotation.
In the UI, an ellipsis may follow the label for an affordance to indicate that further refinement of the action will be made via subsequent selections. For example, Open… is sometimes displayed this way because the user will next select what to open. Do not include the trailing ellipsis in user documentation.
Do
We the People of the United States … do ordain and establish this Constitution for
the United States
of America.
Click Open and select a file.
Don't
Don't: Click Open… and select a file.