You are right that a black hole as such is almost impossible to detect. The black hole itself does not radiate anything much except Hawking radiation which is "darker" than the ubiquitous cosmic microwave background. A nearby large back hole, if one could withstand the spacetime distortions, would be a "dark patch" in front of the faintly "glowing" (in the microwave range) background.
Another way large black holes betray their existence is by distorting light, even acting as a cosmic magnification glass when the stars align just right. But this effect is visible for large black holes only and needs scrutiny to detect.
Yet another detectable "direct" effect is the spacetime vibration caused by collisions of black holes. It is a bit like being inside the pool when somebody butt-dives into it on the other end. But we have only been able to detect these vibrations for less than a decade (and the Caltech and MIT guys got a Nobel prize for it, like, immediately).1
Because a black hole as such (and the reason for this repeated caveat is below) is practically invisible there is even speculation whether there is a much larger number of them than generally assumed.
The reason I say that black holes "as such" are invisible is that there is a class of black holes which make their existence unmistakably known: They are quasars, the brightest objects ever, by far. They spit out radiation and matter at relativistic speeds over many lightyears, enough to disturb their host galaxies and put their imprint on entire cosmic neighborhoods. You are right: The light and matter in these jets does not emanate from within the Schwarzschild radius, that would be impossible. It emanates form the extreme conditions around the black holes, which fuel extreme interactions with and between matter in its vicinity. The black hole is a bit like your blender when you forget to put the lid on: It ruins the entire kitchen, the more is in it, the merrier. The blender as such isn't doing anything, really ;-).
But when it has things to shred, it becomes very visible.
1 Well, almost immediately after their successful experiment. But that was the result of decades of preparation.