It is difficult to remember cases. The easiest way to remember cases to learn a proverb. Иван Родил Девчонку Велел Тащить Пеленку. Именительный, Родительный, Дательный, Винительный, Творительный, Предложный падежи.

I don't remember it too)) http://bitclass.ru/rus/theory/%D0%9C%D0%BE%D1%80%D1%84%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F/%D0%9F%D0%B0%D0%B4%D0%B5%D0%B6%D0%B8

For me, there is no way to learn Russian cases "fast." Instead, the way I learned Russian cases is slowly and a little at a time. For example, I worked on ONE case at a time and ONLY on hard stem masculine nouns. When I knew that well, I then worked on hard stem feminine nouns and then when I knew that, I worked on neuter nouns. Then I worked on soft-stem endings for masculine nouns and then for feminine nouns. Also, I never tried to memorize a single word or case ending. Instead, I learned each case in a short sentence with a word that that I already knew, a simple object that was in front of me. This made it much easier to remember the case ending because I was describing what I was seeing. For example, for the accusative case, "I see a telephone, I see a pencil, I see a table. All these nouns are masculine in Russian with hard stem endings -- consonants -- for inanimate nouns in the nominative and accusative cases. Next I learned feminine nouns in the accusative case: I see a cup, I see a book, I see a newspaper (all end in "a" in the nominative case and in "y" in the accusative case). For the prepositional case, I see the telephone on the table. I see the pencil on the table. By breaking down each case by gender and hard vs. soft stem (and inanimate vs. animate nouns for the accusative case) AND -- very importantly -- by using each noun in a short sentence, it was easy to remember the case endings. It's only hard if you try to learn too much at once. Using objects that were in front of me kept it interesting because I wanted to describe what I saw. It was not abstract memorization which for me is boring and not effective. Cases are not something to learn in a couple of days, weeks or months because you also have to learn when to use each one which for some of the cases is complicated. Read as many simple texts (or listen to beginner Russian Youtube videos) so that you see and hear how the cases are used also greatly helps.

i just realized that Russian language really complicated for studying) Never thought about this before. Maybe tables will be more appropriate. Like this: https://www.google.com.ua/search?q=russian+cases&espv=2&biw=1745&bih=905&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiFr6nzn63RAhWBDCwKHfQODpMQ_AUIBigB#imgrc=AK89Uu_sfBqvCM%3A But the main thing is practice. Contr question: how can I know which vowels I should use when reading persian words?

Don't Farsi have cases? I learned little Uzbek, and it have 6 cases too. Try this site: http://www.russianlessons.net/. You have to understand cases, not just remember these.