It's a bit more manageable if you can see all the declensions of a word sorted into a table: (scroll down to Declension and click "show")
Every lesson have some tips and notes, but they are only visible in the web app. https://www.duolingo.com/skill/ru/Genitive-Case---1
Tips and notes
In Russian “I have” is expressed by «У меня (есть)» structure. The owner is in the Genitive case.
"The of-case". It is one of the most universal cases. How do you make the forms? Here is the regular pattern:
A zero ending means that the word ends in a consonant or a soft sign (which is just a way to show the final consonant is "soft"). In the Nominative singular, a Russian word can only have the following endings: а, я, о, е, ё ornothing ("zero ending").
GENITIVE OF NEGATION
If you use «нет» to say that there is "no" something or you do not have it, the object is always in Genitive:
У меня́ есть я́блоко → У меня́ нет я́блока
Здесь есть рюкза́к → Здесь нет рюкзака́.
"of" (possession): яблоко мамы = mom's apple"of" (amount): чашка чая, много чая = a cup of tea, a lot of tea
A huge number of prepositions requires this case. Yes, «у меня есть», «У неё есть» only use «меня» and «неё» because «у» wants Genitive.
For он, она and оно Genitive doubles as a non-changing possessive "his", "her", "their": его, её, их.
initial «н» is used for him/her/them with the majority of prepositions (doesn't affect possessives)
A little side note: some nouns of foreign origin are indeclinable. It means that all their forms are the same. Foreign nouns that end in о/е become like that (кофе, метро, радио, резюме), as well as all nouns that do not fit into Russian declension patterns (see above).
This includes female names that end in anything other than А or Я. A few -ь-ending names are an exception (Любовь and Biblical names like Юдифь).
So, all of the following names are automatically indeclinable: Маргарет, Мэри, Элли, Дженни, Рэйчел, Натали, Энн, Ким, Тесс, Жасмин.
I AM AWAY
Russian also uses the Genitive to state that someone is "away", "not there": Мамы сейчас нет. In English such use would correspond to "There is no mom at the moment", or even "There is no me now". We are not hard on that particular construction in the course, but it is important to know it all the same.
Added bonus: when a verb directly acts on a noun, the noun is called a direct object and is in Accusative. In Russian, only -а/-я feminine nouns have a unique form for it. Others just reuse Genitive or don't change the word at all (Nominative)
Russian uses.... let's call it "consistent" negation. It means that in negative sentences you are required to use "nothing" instead of "anything", "nowhere" instead of "somewhere" and so on. Let's meet the first of these pronouns:
У меня ничего нет. = I don't have anything. Она ничего не ест. = She doesn't eat anything.
You'll also notice that, unlike standard English, Russian has no rule against using double negatives.
Right. Never write кы, гы, хы, etc [EDIT: see post below for clarification and details]. Always ки, ги, хи instead. With к, г,х it sounds as written (и). With Ж and Ш [EDIT: ч, щ were accidentally included here initially, see the post below] it is still pronounced as if it were ы, but is written like и anyway for historical reasons (like the pointless ь after ш on every verb in the ты conjugation, which does not affect ш at all).
You are absolutely correct there. I knew that myself, but it completely slipped my mind here. I clearly got confused because of the rule that you never write "ы" after Ж, Ч, Ш, Щ, so I put all of them together there, but the pronunciation rule that I cite applies only to ж and ш. In general ч, щ are always soft, and ж, ш, ц are always hard (though writing ци and цы are both possible and not forbidden by a spelling rule, but ци sounds like цы).
I gave you ten lingots because this is really important stuff that could really confuse beginners, good eye there :). I'll adjust the original post accordingly.
Here is wikipedia's entry on the spelling rules:
Cyril and his companion were a couple of bad persons. They didn't reproduce the phonetics on single items! Russian is terrible like French! I love Japanese (Italian and Spanish for the most), what you write is what you read what you tell is what you write, one letter one sound one sound one letter.
In music the same language is used by musicians. The scientific community uses Latin. Computers use English as common language. Why humans do not use a common language?. Because they have invented a concept called national or group identity. It could be accepted, but on the other hand creates communication barriers and jobs for many people.
Is this usage a standard negative in British English? If so, maybe question it to the makers of Duolingo. Duolingo is headquartered in Pittsburgh, Pennsylvania, and goes with the standard negative in American English, which, as Alexmalaho says above, requires the helping verb "don't". But Duolingo shouldn't discriminate against language norms in other parts of the globe. If I'm wrong, and this isn't a British usage, please ignore!
Can I ask whether a more accurate translatiom of this " У собаки нет воды " is "the dog does not have water" or "the dog has no water"? They both are marked as correct, however I know the difference is subtle but there in English, because one is saying it does not exist in their possession the other is giving the amount which is none. If it is one of those, how do you say the other in Russian?
The grammatical case depends on the function of the word, not on it's position within the sentence, so the cases and the word order are pretty unrelated. Depending on what you are trying to say the noun in the genitive case can be in the beginning, in the middle or in the end of the sentence.