I used to say that grammar is not that important for acquiring a new language. This is true. Knowing linguistic slang doesn't help you to become fluent in any language including your native one. Practice does. However, as I learned from my teaching experience, for some students it is quite useful to understand the basic logic that lies behind the over-complicated Russian grammar rules. This is why I decided to make a brief observation on how the Russian grammar describes or, better to say, categorizes the world.
Words mean something more or less material. There is something in the real world, and we have a word for it - this is how any language works. Besides, words have grammatical meaning - the meaning that is needed to build an intelligible sentence, to show the relations between words in a sentence. In English, you have a word order to do this job, and endings are not that much needed (Love is all you need. vs. Need is all you love). In Russian, the regular meaning (semantic) is normally placed in a word root, while grammatical meaning is concentrated in its ending. In short: roots (and, sometimes, affixes) are for saying what you want to say, and ending are for connecting words together.
Русский (Russian) - the root Русс- is for Russ-, suffix -к- is for adjective, and ending -ий is for masculine, singular, nominative
Grammar divides everything into the two big categories - things (nouns) and actions (verbs). Verbs stand for actions. Verbs show who acts (I myself, you or someone else, a grammatical category of person), does he/she/it acts alone or in a company (number), where in time the action takes place - past, present or future. Take a Russian verb, find its ending - and you'll see what person, number and tense a verb is. For example: бегут (are running) - the ending is -ут, which is a regular ending for 3-rd person, plural (they), present tense. In the Past tense, Russian verbs have gender, but don't have person. For example: бежaла (was running) - the ending -ла is for Past, feminine for all the three persons. Я бежала (I was running), ты бежала (you were running), она бежала (she was running).
The verb ending -ут is for present, third person, plural (they)
Nouns which stand for things can be singular or plural, which is quite understandable: you either have one flower or many, one stripe of bacon or many, one hand or... Hmm.. Well, a few centuries ago, there was the third grammatical number in Russian - the dual number, but it vanished completely (good news, you have fewer endings to memorize). Also nouns could be masculine, feminine or neuter. Grammatical gender is not equal to sex, so there's no logic behind defining revolution (революция) as feminine, and pollution (загрязнение) as neuter. The third grammatical attribute that each noun has is a case. What is a case? A case shows how one thing relates to other things in a sentence. For example, if a nous is a subject, i.e. something or someone who acts, you should put a noun into the Nominative case. If a noun is a direct object, out it into Accusative. Same in English: She (nominative) see me(accusative). So, each noun has a gender, number and a case.
Things may have some features or attributes. Adjectives are what you have to use if you want to make your language more colorful and descriptive. I've heard a term “modifiers”, but I don't like it. Adjectives do not modify nouns, they describe nouns. Adjectives in Russian are not quite independent, they 'belong' to a noun. Thus they inherit grammar attributes from a noun, its gender, number and case. The rule is very simple: put the corresponding adjective into the same gender, number and case with its noun.
You can perform an action in this or that fashion. For describing how exactly you perform an action, Russian has adverbs. Adverbs is my favorite part of speech, because it has no grammar categories except of degree of congruence. You run fast (быстро), and you can run faster (быстрее).
Of course, knowing that Russian nouns have six cases won't help you to learn Russian, but, probably, my article will help you to accept the reality of Russian grammar.