To clarify the other comment, the word "нет" has more than one meaning. It does not only mean "no". It can also mean (literally) "there is no", so the phrase "у меня нет молока" translates to "with me there is no milk". Contrary to English, this is actually the more natural/prevalent word order in Russian.
No, it's genitive. In the construction «нет» + noun, used to express absence, we put the noun in genitive.
No, if I were to say you have a milk, I would say «у тебя́ е́сть молоко́» (you have milk; literally 'at you is milk') and it would be in Nominative.
У is a preposition to introduce the possessor. It's basic meaning is 'at' or 'near', but in this sentence «у тебя» could be translated 'at you possession'. I.e. «У тебя́ нет молока́» = 'At you[r possession], there-is-no milk.'
In other contexts, «у тебя́» can mean 'at your place'. For example, «Мо́жно я переночу́ю у тебя́?» 'Is it OK if I sleep over at your place?'.
So you get the meaning ('you', 'we' or anything else) by looking at the word following the preposition:
- у тебя = at your possession, at your place (informal),
- у вас = at your possession, at your place (formal or plural),
- у нас = at our possession, at our place.
Pardon this reply being out of date.
I just submitted "You don't have the milk" and it was not accepted.
By "we", did you mean native English speakers? That'd be useful information. Also, I disagree with milk being uncountable. If you're in a restaurant you can order milk as a beverage and say "I'll have a milk" or "Two milks, please."
Both of these situations may be totally different in Russian, though.
The inverted negative ("you have not", for example), was once the norm in the English language for all verbs but has long been archaic to the point of sounding incorrect to most English-speaking ears. Now we always place "do" as a dummy verb in its place, with the bare infinitive. As a result, "do" is virtually the only verb you place before "not" when forming a negative. (There are some poetic, ironic and literary exceptions, but they are special cases.)
"I have not" - "I do not" + "have"