The science of classifying and identifying organisms is called taxonomy. It is a hierarchical system that groups organisms into seven major categories. In descending order they are: kingdom, phylum, class, order, family, genus and species.
The taxonomic system in use today was designed in the 18th century by Carolus Linnaeus. It uses a combination of the genus name and the species name to derive the scientific name of an organism. For example, the scientific name for a house cat is Felis catus. Felis is the genus and catus is the species.
Taxonomy is a good way to show how closely organisms are related. Dogs are classified as Canis familiaris and wolves are Canis lupus. Though these two animals are different species, they belong to the same genus and thus are closely related.