Look for matter. Using images and data from the Hubble Space Telescope, you will see rings of gas and dust around a black hole. Depending on how big the black hole is, you may be able to see a swirling disk of stars as well.
Measure radiation from the matter around the black hole. Energy will come from the accretion disk following the law of conservation of angular momentum, the jet producing feedback and the radiation as objects get hotter and more violent. Optical light will be emitted from the accretion disk and x-rays will be visible on the inner edge.
View light sources from a spectrograph. The Hubble Space Telescope holds an instrument called the Space Telescope Imaging Spectrograph. When studying the data from this spectrograph, you can see a rainbow pattern that sheds light upon how fast the starts and gas are swirling. It can also give you the specific location of the swirling stars and the black hole itself. The faster the stars go, the more massive the black hole must be.