The American Goldfinch male is a vibrant yellow in the summer and an olive color during the winter, while the female is a dull yellow-brown shade which brightens only slightly during the summer. The male displays brightly colored plumage during the breeding season to attract a mate.
American Goldfinches molt twice a year: once in the autumn and once in the spring.. Once the spring molt is complete, the body of the male is a brilliant lemon yellow, a color produced by pigments from plant materials in its diet, with a striking jet black cap and white rump that is visible during flight. The female is mostly brown, lighter on the underside with a yellow bib. After the autumn molt, the bright summer feathers are replaced by duller plumage, becoming buff below and olive-brown above, with a pale yellow face and bib.
Goldfinches are migratory, but can be found here in Georgia at feeders all year long. They will sometimes descend in flocks in the spring and fill the trees and shrubs with their chatter. They will mob a bird feeder, preferring nyjer (thistle) and sunflower seed. 
Adult Goldfinches are strict vegetarians and will not eat insects except occasionally by mistake.
The American Goldfinch begins its breeding season later in the year than any other finch and later than any other native North American bird except, occasionally, the sedge wren. Their breeding season is tied to the peak of their food supply, beginning in late July, which is relatively late.
Their nest is built in late summer by the female in the branches of a deciduous shrub or tree at a height of up to 30 feet. The inside diameter of the finished nest is about 2 1/2 inches. The rim is reinforced with bark bound by spiderwebs and caterpillar silk, and the cup is lined with plant down from milkweed, thistle, or cattail. The nest is so tightly woven that it can hold water, and it’s possible for nestlings to drown following a rainstorm if the parents don’t cover the nest.
The chicks hatch 12–14 days after incubation begins. The hatchlings develop quickly, opening their eyes after three days, and completing the growth of olive-brown juvenile plumage after 11–15 days, at which time they begin to practice short flights close to the nest. Then, they join their parents at bird feeders, which is why you’ll notice a spike in the number of Goldfinches in August.
References and Additional Information
 Wikipedia: American Goldfinch
 Cornell – All About Birds: American Goldfinch
 The Intown Hawk – post: An Abundance of Gold
 The Intown Hawk – post: Late Starters
 Wikipedia: Guizotia abyssinica (Nyjer)