"много собак"
Translation:a lot of dogs
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I think this is actually the MOST intuitive way to use the genitive. Translating the cases to English often benefits from the use of additional "helping words."
A good rule of thumb is that (aside from certain specific constructions) a genitive is often best translated as "of ____." So много = a lot, собак (gen. pl.) = of dogs. много собак = a lot of dogs.
It also works when the genitive is used to show possession if you think of it in terms of "Peter's dog" being "the dog of Peter."
Similarly, translating the dative frequently uses "to" or "for," and the instrumental can use "by" or "with."
Even in instances where the helping word isn't strictly needed or may not be the BEST translation, I find it helps me remember how to use and identify the cases.
It's not an ending. «Собак» has zero ending; zero ending shows it's a genitive plural form in this case.
I think you know what plural is, English nouns also can be plural and singular (dogs vs. dog), so only 'genitive' is left to explain.
Russian nouns have several case forms (6 of them, according to the most common classification). Each form is used to convey some grammatical meaning.
Nominative is the most basic form, it's used for the grammatical subject of the sentence (соба́ка сиди́т 'the dog is sitting') and for the predicate in «X is Y» sentences (in «соба́ка зла́я» 'dog is angry', both собака and злая are nominative).
Genitive is often translated with the 'of' proposition, or it's sometimes translated with the English possessive case: соба́ка сестры́ sister's dog (сестры is genitive). However, it has a number of other uses: notably, after «нет» is is used to express absence.
Dative corresponds to the English preposition 'for': соба́ке 'to dog'.
Listing all the cases and their functions here might not be useful, as you'll learn all of them as you progress through the course. To get a list of all the case forms, you could use Wiktionary: https://en.wiktionary.org/wiki/%D1%81%D0%BE%D0%B1%D0%B0%D0%BA%D0%B0#Declension