How would a small TCO (temporarily captured orbiter) or other natural Earth satellite most likely be detected?
Cruithne and J002E3 were detected using ground based astrophotography.
J002E3 is thought to be "the S-IVB third stage of the Apollo 12 Saturn V rocket ... It is thought that J002E3 left Earth orbit in June 2003, and that it may return to orbit the Earth in the mid-2040s.1"
Ground telescope also found 6Q0B44E which orbits beyond the moon.
2002 AA29 was found via automatic sky survey.
Several of these objects are in horseshoe orbits.

Regardless, the discovery of these objects usually comes via conventional astrophotography.