Although we cannot see black holes, we know they are there because of the effect they have on their surroundings. When matter falls towards a black hole, it emits electromagnetic radiation. Scientists use tools like the Chandra X-Ray Observatory (http://chandra.harvard.edu/index.html) to see radiation emitted around black holes and other space phenomena that is invisible to our human eyes.
Black holes have such enormous gravitational forces that even light cannot escape. When a black hole is in the way of our view of, say, another galaxy, it distorts the light and bends it around itself.
Wikipedia has a great animation of gravitational lensing: http://en.wikipedia.org/wiki/File:Black_hole_lensing_web.gif
|A black hole distorting the light from the galaxy behind it. This is called "gravitational lensing".|
|Image from BC Science 9 Textbook|
"A black hole's effects on its surroundings. A star is being drawn into the black hole, and jets of material are shooting out the center."