Use de with common nouns (masc. / fem.) and het with neuter nouns.
Always use de with plural nouns.
Du does not exist in modern standard Dutch. It's basically the equivalent of thou in English and as such has been replaced by jij/gij.
I wrote the women speaks/talks - which of course was wrong. Can someone explain to me what that would be in Dutch?
That is not a correct English sentence. "Women" is plural and the forms "speaks" and "talks" are only used for singular subjects. Assuming you meant the singular "woman", it would be:
- De vrouw spreekt - The woman speaks
Is it not also correct to translate this "The women are speaking."? I understand that it does not read "De vrouwen zijn aan het spreken.". But, is it incorrect to translate "De vrouwen spreken" in present progressive?