What's the best way to learn all the cases in Ukrainian?
I have had a few teachers back in Lviv, and they just expected me to learn it ...but I didn't understand why they were used in different situations...obviously I get the Він. вона і вони most of the time at least

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Leigh, добрий вечір!
Забудь про англійську! Відкладемо в сторону фонетику, вимову. Набирай шаблонні вирази, як говорять українці. Українською треба сказати так!!! Не перекладай - ми говоримо не так, як Ви! Друге - щільно працюй над українською лексикою. У нас море синонімів, та вони відрізняються один від одного і іноземцеві тяжко осягти тонкощі висловів. Там, де у людей одне слово - у нас два, де у людей два - у нас п'ять слів. Крім каторжної роботи над лексикою і над нашими виразами та фразеологізмами нічого не можу порадити. Переступити поріг української надто складно. Дай, Боже, духу тобі здолати цей поріг.

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I'd suggest to learn the cases from an Ukrainian grammar book with examples in Ukrainian, while thinking of en equivalent you would use in English. And as you live in Ukraine (you still do, do you?) use all those sample sentences in your daily conversation until they are obvious to you (until you don't stop to pick up the correct case, I mean).

Another good way - to write a list (or couple of lists) of sentences you use in daily conversation in English and get those translated by native speakers into Ukrainian and than just use it until ... :)

Or try composing a scheme: Ukrainian case  -> sample sentences in Ukrainian -> possible equivalents in English.

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you don't hear the endings or you cannot pick up a proper one when speaking yourself?

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Yeah I mean nominative, accusative ....
The problem is that I taught English in Lviv for 3.5 years, and I couldn't fine a teacher who could teacher it properly (for an English speaker) so I taught myself. I can get what I want to say understood, but I know I am not getting the endings correct..)

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What do you mean by cases? Nominative case, accusative case, dative case, ablative case etc.? Or pronouns - I, you, he, she, it etc.? Or maybe you want to learn how to decline pronouns in Ukrainian (eg., I - me - to me - by me etc.). I believe that as soon as you will have a clear image of WHAT you want to learn it would be at least a big part of answer HOW to do it easy & quickly. ;)