The easiest way to correlate a meteorite with a parent body is, when the parent body still exists. This is the case for Lunar and Martian meteorites. Samples from Lunar meteorites can be compared with samples from the Apollo program. Martian meteorites can be compared to analysis carried out by rovers (e.g. Curiosity).
Meteorites can also be compared to spectral classes of asteroids. In order to identify the parent body of a class of meteorites, scientists compare their albedo and spectra with other known bodies. These studies show that some meteorite classes are closely related to some asteroids. The HED meteorites for example are correlated with 4 Vesta.