"The girl has no water."
Translation:У девочки нет воды.
У (genitive) нет (genitive)
У девочка(-а+ы-ы+и) нет вода(-а+ы)
У девочки нет воды
http://www.russianlessons.net/grammar/spelling_rules.php (Spelling Rule 1: Ы - И)
I am no expert, but I got this: When you are talking about something that the subject owns (like "the girl has a book"), you use есть When you are talking about something the subject lacks (like in this case, "the girl has no water", or "the girl does not have water"), you use нет. I hope it was of help!
At this point I imagine this to be the conversation of Duoling zoo workers... they have all these cages everywhere with men, women, children, girls and boys, dogs, horses and weirder stuff... And they keep reminding each other: "Look, the girl didn't get her daily dose of apples and bread yet." "The horses have no water!"
It's a specific structure. In English you use [possessor] have/has, and in Russian it's У [possessor in Genitive] есть [noun in Nom.] or нет [noun in Gen.]. So, in this sentence the girl is a possessor and she does not have water, so вода is in Genitive.
You can actually use имеет, but it's usually reserved for some official declaration, like "Citizens should have passports when crossing borders" or whatnot, but people don't use it in everyday speech (btw, Russian has too many of those words which they use only officially and never in everyday speech ;-) )
If you say it in normal speech, you risk of sounding way too pretentious.