A black hole have only its gravitational field to make itself known to us, and that gravitational field creates only three observable effects: it can change the brightness of more distant objects, it can cause matter to release gravitational potential energy as radiation, and it can affect the orbits of nearby stars.
Most black holes are solitary, which effectively places them beyond our sight. Born in the collapse of extremely massive stars, they should number less than the number of solar-mass stars in our galaxy, so the nearest black hole should be at least several parsecs away from Earth. Their masses must be greater than about 3 solar masses, and perhaps greater than 5 solar masses; anything less massive would collapse to a neutron star. Because a solitary black hole produces negligible radiation, it can only be found through its effect on the brightness of more distant stars. The difficulty in identifying a black hole in this way is that a black hole's effect on the brightness of more-distant stars is indistinguishable from that of a normal star of the same mass. The Einstein ring of a black hole and of a normal star of the same mass are identical; at a parsec, it is too small to resolve with a telescope. The radius on the sky of the last stable orbit of a black hole is factors of ten smaller than the radius of the Einstein ring, so the one telltale feature of a black hole, the repeated images of the sky that encircle the black hole, would be invisible from Earth.
In principle, one could search for black holes in a gravitational lens search. These searches try to find a dark object within our own Galaxy by watching for a brightening in stars in other galaxies; the current gravitational lens searches find low-mass stars and brown dwarfs. When a object within our galaxy passes between Earth and a star in a distant galaxy, the star becomes brighter for a period of time that depends on the mass and distance of the object causing the brightening. For a 5 solar mass black hole at a distance of 10 kpc, a star would become bright for about a year. Searching for lenses created by a black hole would therefore be a very long-term undertaking. On the other hand, they could be distinguished from the lens created by a main-sequence star from the absence of light; at 10 kpc, a star of 5 solar masses should have a magnitude of about magnitude 18, which could be seen by a large telescope if it were well out of the dust of the Galactic plane. The value of such a study would be limited. This type of study could not distinguish between neutron stars and black holes, and any estimates of mass would depend on assumptions about the distance and velocity to the object. Without a clear signature of a black hole, the study would only give an estimate of the number of such bodies within the Galaxy.
The only truly effective method of finding a black hole is to look for black holes made luminous as they pull gas onto themselves. This process can turn a black hole into a brilliant beacon visible across the universe. The potential well of a black hole is so deep that when gas falls into it, the amount of potential energy liberate and radiated away is a substantial fraction of the rest mass energy of the gas. If we could dump 10-12 solar masses onto a black hole, we would produce about as much energy as is radiated by the Sun in a year. More important, this energy would appear predominately at x-ray and gamma-ray energies, which can travel to us across the width of the galactic disk without significant absorption by gas and dust. The only real question is where does one find the conditions that cause a black hole to light up? There are two places to look: in compact binary star systems, and at the centers of galaxies.
We have many examples of either a neutron star or a degenerate dwarf in close orbit with a main-sequence star and emitting massive amounts of radiation as it pulls gas from its companion onto itself. In such a system, radiation is released as the gas spirals in an accretion disk down to the compact star and as the gas strikes the star's surface. For neutron stars, the gas in an accretion disk emits low energy x-rays from the inner edge of the accretion disk and high energy x-rays and gamma-rays from the star's surface.
The first half of this picture holds up if the central source is a black hole. As with a neutron star, an accretion disk surrounding a black hole should emit x-rays from its inner edge. Unlike the accretion disk around the neutron star, the inner edge of the accretion disk around a black hole is defined by the last stable orbit of the black hole. This inner edge would be the most luminous part of the accretion disk, emitting energy to us as x-rays and gamma-rays.
In practice, we find many x-ray emitting binary systems that are massive enough to contain black holes. Some of these systems are among the brightest x-ray and gamma-ray sources in the sky. All are very far away, generally at a distance of order 10 kpc. What we know of black hole candidates comes from studying these systems. There masses are of order 5 solar masses. We expect the masses to range from 3 solar masses to a couple of hundred solar masses, reflecting the maximum mass of a stable neutron star and the maximum mass of a main-sequence star.
But the binary system is not the only place where a black hole can consume massive amounts of gas. The environment at the center of our Galaxy and at the centers of other galaxies is dense with gas and stars. Gas stripped from stars as they pass each other, as well as gas from the galactic disk, settles to the center of a galaxy. If a black hole sits at the center of a galaxy, it would be lit-up as it pulls gas onto itself. The difference between this black hole and the black hole pulling gas from a companion star is that the black hole at the center of a galaxy should be from a million to a billion times the Sun's mass. We see evidence for such black holes in distant galaxies with brilliant cores. Quasars and Seyfert galaxies are just two types of the host of galaxies that emit massive amounts of energy from their cores. The theory behind these galaxies with bright cores is that a massive black hole is consuming massive quantities of gas. But there is no direct measure of the mass of the black hole candidates in these galaxies, the mass is inferred from the amount of energy radiated by these objects.
The one direct measure of the mass for a black hole candidate at the center of a galaxy is for the object at the center of our own Galaxy. This object, which has the snappy name Sagittarii A* (Sgr A*), is seen by it radio emission. It cannot be seen at optical wavelengths because of the dust between it and us, and it has yet to be positively associated with an x-ray or gamma-ray source. The stars at the center of our galaxy orbit this object with a distribution of velocities that suggest they are orbiting a point mass. Radio measurements of the velocities of these stars gives a mass of 2.6 million solar masses for Sgr A*.
So we see and study two sets of black hole candidates: star-sized black holes in compact binary systems, and black holes of a million solar masses or more at the centers of galaxies. All other black holes are invisible to us.