"The woman has a black dress."
Translation:Die Frau hat ein schwarzes Kleid.
Because the Kleid is not in the genitive case. As something the woman has, it is the direct object of the sentence, and therefore is in the accusative case. A 'das' word in the accusative case gets the affix -es onto an adjective (in this case the colour 'schwarz') but still gets the indefinite article 'ein'. It only becomes 'eines' in the genitive case.
When an object moves to the accusative case, any adjective pertaining to it requires an appropriate suffix. In this case, because "Kleid" is a das word, and it is in the accusative case, we have to change the adjective "schwarz" to "schwarzes". This would apply to basically any adjective we put before "Kleid", not just a colour. So if I wanted to talk about a little dress, instead of a black dress, I would say "Die Frau hat ein kleines Kleid."
This is way easier than anything else to understand the declesion with adjectives: http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html
Eines it would be genetive case in this sentence The haben verb takes Acussative Case and the indefinite article ein forces mixed inlection and the gender of the Noun(Kleid) is neuter.
Mixed inflection+Acussatve case+Neuter Noun=adjective ending=es;
schwarz becomes schwarzes
A noun can be present without an article, preceded by an indefinite article (ein, kein, ...) and preceded by a definite article (der, die, ...). In the second case, you have a Mixed Inflection. You may find explanations and rules of use in : http://en.wikipedia.org/wiki/German_adjectives