Gravitational lensing as discussed in the other answers will indicate whether a massive system is there. Radiation identifiable as coming from the black hole, so as to mask its "blackness", i.e total absorption of radiation, is seen here
This composite image shows powerful radio jets from the supermassive black hole at the center of a galaxy in the Phoenix Cluster inflating huge "bubbles" in the hot, ionized gas surrounding the galaxy. The cavities inside the blue region were imaged by NASA's Chandra X-ray observatory. Hugging the outside of these bubbles, ALMA discovered an unexpected trove of cold gas, the fuel for star formation (red). The background image is from the Hubble Space Telescope
Charged particles, attracted and falling into a black hole, will emit radiation, also particles circulating in the gravitational field of a black hole. Hawking radiation is not in the visible for large black holes so cannot be caught in astronomical measurements. Considering also that the black hole may have a charge or a magnetic field, it is inevitable that part of this radiation will mask the "blackness".
So black holes, as seen above, are calculated to exist behind a curtain of visible radiation, fitted with various models. In the image above the charged particles form plasma jets.
With some patience , we might get a better resolution of how a "physical black hole" looks, in contrast to an artist's image:
After training a network of telescopes stretching from Hawaii to Antarctica to Spain at the heart of our galaxy for five nights running, astronomers said Wednesday they may have snapped the first-ever picture of a black hole.
It will take months to develop the image,...
Already we see that in real life photographs by telescopes of black holes, the blackness is masked . The artists' impressions are really two dimensional cuts in a three dimensional space, which is not something observable without mathematically unfolding data.