There are several methods. See below.
Work Step by Step
If the black hole has a visible star as a partner, we can observe the black hole's gravitational effect on the partner’s orbit. We can detect radiation emitted by matter as it is captured by the black hole (before the material crosses the event horizon). We can measure the effect of the black hole's gravity on light that passes close enough to be deflected (but not close enough to be sucked in). Gravitational-wave astronomy is also a "thing," and gravity waves emitted by two merging black holes have been detected.