The common full name is the basic method of identifying a bird. For example, the Bullock's Oriole is one species of the oriole family.
Many birds are frequently further identified in field guides by their sex, age, and plumage. Often times their plumage is subdivided by breeding plumage and non-breeding plumage. Breeding plumage is typically brighter plumage from mid spring through early fall. Non breeding plumage is a duller plumage from mid fall to early spring. Regarding their age, birds in their first year of life are often called juveniles, with plumage that is not yet fully developed. Immature birds refer to younger birds that does have fully developed plumage but still differs from an older adult.
Keep in mind that all birds have a molting schedule which varies widely but some general patterns can assist with the age determination. Generally birds will undergo two molting periods per year. The majority of molting takes place after breeding, in late summer or early fall; another important molting period for some birds occurs in late winter and early spring. Some larger birds such as gulls and hawks may be molting to some extent in all months. So most birds undergo a complete molt each fall and a partial molt of just their body feathers in spring. Juveniles, on the other hand often only molt their body feathers while retaining their wing and tail feathers until the second fall. This results in a key clue to recognizing birds in their first year: their wind and tail feathers are more worn and faded and often a slightly lighter color than those of an adult (1). Keep in mind there are many exceptions to this general pattern.
For those that want to get really serious, there is of course also the scientific name that each bird belongs to. The scientific name is typically two names. The first is the genus, which is the group that the bird belongs to; the second is the species within the group. Occasionally, a third name identifies a subspecies. Subspecies are populations within a species with consistent variations in plumage, shape, and/or behavior. For example a Bullock's Oriole has the scientific name of Icterus bullockii. Scientific names not your cup of tea? Not to worry though, many many birders do not bother learning the scientific names of the birds. Like anything, you can take it just as far as you like.