Although we cannot directly observe black
holes because light cannot escape from them, we can observe the way black
holes affect their surroundings. Black holes pull in surrounding dust and
gas which when heated emit radio waves, visible light, x-rays and even
gamma rays that we can detect. Also, we can directly observe
the accretion disk and the jets formed from black holes with modern telescopes
such as the Hubble.
X-Ray/Gamma Ray Emmission
As you know, a black hole pull in surrounding matter
such as gas and star dust which forms an accretion disk around its event
horizon. The potential energy of this matter then converts into heat energy.
Because of the black holes deep gravitational well, the matter is heated
to superhot temperatures, which emits high energy X-rays or even gamma
rays. This radiation can observed with modern X-ray telescopes.