If a US citizen (or any citizen in a country with a similar system) is targeted by a secret warrant from something like the FISA court, how can they know and how can they defend themselves? Is there some method or do you just have to hope that nobody mistakes you for a bad guy?
There is no general means for a person to determine that he is of has been the target of a surveillance warrant request. You can read details of the Foreign Intelligence Surveillance Act. Even apart from national security cases, the police don't notify mobsters that they are being wiretapped, when they have a warrant. The Act expands police powers for certain specific kinds of cases, for example, POTUS can authorize the Attorney General to collect information without a warrant for up to a year provided that it is only to collect foreign intelligence information, as long as there is not a substantial likelihood that a United States person is a party to such communication. Or, a warrant will be granted if the surveillance targets a foreign power or agents of a foreign power. It is difficult to track the exact rules which change, in part via secret rulings from the Foreign Intelligence Surveillance Court such as the 2011 ruling that allowed the NSA to search communications of Americans.