First, never before in history will the sky have been searched so thoroughly (for example, by Ohio State, the Harvard/Planetary Society, NASA and the Soviet SETI projects). Also, the Planetary Society is now discussing with Argentina the possibility of establishing a Southern Hemisphere SETI.
Second, an advanced civilization may use a sizable fraction of its sun's energy output. This may lead to detectable side effects, just as our radio, radar, TV and atmospheric nuclear weapons tests have produced inadvertent signals an alien astronomer might find.
Third, the numerous Earth- and space-based observatories could find the first signs of another civilization in some puzzling astronomical phenomenon.
Fourth, a communications engineer could detect a celestial noise source that turns out to be from another civilization.
Fifth, amateur SETI projects in the United States and Canada might find a signal on a frequency the professionals have dismissed for incorrect reasons.
Sixth, military electronic ...