As is the case with most of our avian friends, the hens and cocks can be differentiated by their colors. This is called sexual dimorphism. Cocks are much more colorful than their female counterparts. This is the result of natural selection over the course of millions of years, hens look for the male with the most striking colors when choosing a mate. Hens have a more dull set of feathers because, amongst several other reasons, this allows them to be more well hidden when sitting on their eggs in the nest.
A pair of Zebra finches
Cocks sport several markings that are completely absent in hens - Orange cheek patches, thorat stripes, a black bar on the breast and flanks with a chestnut brown color dotted by white spots. Hens have grey feathers in these areas. Cocks also have a bright red beak whereas hens have more of an orange beak. Fledglings have the same coloration as hens, even if they are male, the one key difference is that the fledglings have black beaks which only bloom into their adult colors at around 90 days old or so.
With the large differences in plumage across the domesticated zebra finch variations, the classical male/female distinctions can be less obvious.