(This is a continuation of the previous post)
In the past I have recommended that people learn as much of the language before their arrival as possible. I would like to revise that. If you can set up language lessons immediately after arrival, then it is probably a better use of your time and energy to just come a few days or weeks earlier and fill that extra time with language study with a tutor, rather than trying (usually unsuccessfully) to find time for independent study while you are busy preparing for your trip. Learning in advance takes more self-discipline than learning on location, and is typically less effective.
My goal for learning Ukrainian or Russian would be very concrete. You need to get over the initial learning hump as quickly as possible so that your knowledge of the language can carry you from there without too much additional effort. Once you are already speaking in the language and understand a large amount of what is being said, moving onward from there is much easier and doesn't require a lot of willpower and study. All that is needed is simply to have people to talk to in the language for a minimum of half an hour to an hour a day and to have a good dictionary (more on this below).
It can take 2 months or less to reach this threshold of somewhere between 1000 and 2000 words (I'd say roughly 1600), or it can take years or even forever if the right conditions or willpower are lacking. If your approach is effective (more on this below), you can assimilate these 1600 or so most useful and oft-repeated words — which I call the "communicative core" of a language — with 150-200 hours of work, which can be compressed into as little as 1.5-3 months. If the process is too drawn out and you keep getting distracted, you may end up taking much longer to get there in terms of hours of effort invested.
If at all possible, I would try to find an independent Russian/Ukrainian tutor in advance or sign up for beginning group classes with a reputable school of Russian/Ukrainian. I would also get some kind of beginning-to-intermediate audiocourse and an electronic dictionary for personal use to complement classwork (more on this below). I would arrange for classes on a near-daily basis. If you're meeting fewer than 3 times a week, it will be easy to lose momentum between lessons.
The order in which you learn things is very important. It is important to focus on what is relevant to your life right now unless you are a bookworm who gets carried away learning the structural nuances of a language. Here is the order I would attack Ukrainian or Russian.
1. The most basic phrases (days 1-2). Things like "hello," "thank you," "please," "excuse me," "do you speak English?", "I don't speak Russian/Ukrainian," "I don't understand," "my name is…", etc., plus very basic grammar associated with these phrases — i.e. conjugating the verbs "to speak" and "to understand," pronouns, and a brief introduction to the most basic grammar principles of Russian/Ukrainian.
2. Cyrillic alphabet + pronunciation (days 2-3). Alphabet and pronunciation go together. Learn all the letters and their best approximate pronunciation. Learn how to write and pronounce your own name. Practice reading some of the signs you'll see all over town ("ресторан," "гастроном," "банк," etc.) and learn what they mean. From here on you can practice reading signs around town and look up or ask your teacher what they mean. Practice repeating words slowly after your teacher to try to grasp the proper pronunciation. Your teacher needs to be sufficiently patient and to be able to explain and demonstrate some of the difficult sounds now and in the future as necessary. It is important to introduce good pronunciation habits from the outset because it will make speaking easier after an initial "break-in" period. Note: all words learned should have accent marks above accented syllables, and nouns should be noted as masculine, feminine, or neuter.
3. An additional complication for Ukraine is that in many mostly Russian-speaking cities almost all the signs are in Ukrainian. This will cost you a bit of time early on, but if you're learning Russian you'll need to learn the Russian equivalents of the words on the signs you're seeing around town (weeks 1-2). Usually the words are very similar, so it shouldn't be terribly difficult. At some point later on (weeks 5-8?) you will also need to learn the fairly short list of differences in pronunciation of Cyrillic letters in Ukrainian vs. Russian, and if you are in a city where much Ukrainian is spoken (Kiev), near the end of the course (weeks 7-8?) it will be very useful to be introduced to the most basic Ukrainian vocabulary (same stuff you learned in the first couple days of Russian classes).
4. Basic vocabulary for specific everyday needs. About 150-200 words at first (weeks 1-2), growing to 2 or 3 times that number by the time you've assimilated the full "communicative core" of 1600 or so words, including names of things you need to buy (groceries, milk, water, beer, banana, ticket, phone card, etc.) or often need to refer to (mobile phone, computer, Internet, wi-fi, apartment, city center, metro, train station, marshrutka, bus stop, office, school, organization, etc.), basic professions and roles (teacher, student, programmer, volunteer, father, mother, children, etc. depending on your activities), countries, nationalities, and languages (America, English, German, Ukrainian, Ukraine, Kiev, France, French, Russia, etc. depending on where you're from), and the "connective vocabulary" necessary to use them ("I am a ___," "I speak ___," "I am from ___," "Do you have ___," "where is ___?", etc., to go, to buy, to want, to be able, to need, etc.), as well as just enough grammar to understand why you say these things the way you do in Russian/Ukrainian. All this new vocabulary should be written in Cyrillic. This will slow things down compared to using transliteration, but it will be much more effective in the long run because you will learn to read, write, and pronounce better in the process.
5. Remaining basic general vocabulary for general communication (1000+ words). The most basic all-purpose vocabulary (my, your, me, him, her, it, that, who, what, when, where, why, because, here, there, today, now, again, at, in, on, etc., as well as numbers) should be introduced in weeks 1-2 with subsequent general vocabulary building upon previous words in order of usage and importance. For instance, "to forget" is appropriate for weeks 5-6 of an 8-week course designed to teach you the communicative core, but not for weeks 1-2. Months, days of the week, and telling time are appropriate for weeks 3-4, but talking about years ("in 1998," etc.) is for weeks 5-8. Grammar principles should be introduced as needed to create and explain dialogues appropriate to your level and current needs. Under no circumstances should your course commence with charts of endings and conjugations. You risk becoming discouraged and delaying your attainment of the communicative threshold by months or years. Introduced bit by bit in the context of things you have heard Ukrainians say or things you need to say yourself, Ukrainian or Russian grammar will be much more accessible and easy to grasp. Vocabulary and grammar that is timely is assimilated much better than untimely vocabulary and grammar. Remember that the connections between words are just as important as the words themselves; if you just know words and no constructions, then you will not be able to guess how to say things as simple as, "I need more time" or "I have a son." General vocabulary should be introduced along with common constructions for using it.
6. Along the way from the beginning to the end, it is necessary to have considerable amounts of unstructured exposure to the language outside of class. This is necessary so that your audial memory can engage in the language learning process by telling you things like "hey, I've heard that word before" and "what does «давай!» mean?" as well as gaining an intuitive feeling for how the language is spoken. Much of this can be achieved by walking around town and going about your daily activities (going to the store, restaurants, cafes, work, parties, people's houses, etc.), but the process can be sped up if you also spend time listening to special dialogues designed for the beginner or intermediate level. These dialogues will be spoken more clearly and slowly and will contain more of the words you have learned or will learn soon in class, so you will be able to get more out of them more quickly. I find it best when the dialogues are exclusively in the foreign language. If they are a complement to studies with a teacher or tutor, then an accompanying textbook is not necessary. If you find you are curious about grammar "ahead of schedule," then look for a grammar textbook to peruse on your own. But don't overdo it and get stressed out by all the things you don't understand. Just use it to satisfy your curiosity and get a second explanation of things in addition to what your teacher has told you, nothing more. Grammar study should assist speaking and comprehension, not vice versa.
7. You will also need a good dictionary — paper or electronic — to be able to look up words on your own. But you shouldn't get too carried away with this process. If you start writing down lots of words that you have not yet heard spoken (i.e. your audial memory is not yet engaged), chances are you will not be able to incorporate them into your active vocabulary until you actually start hearing them spoken around you. Therefore, focus on words you have heard or keep seeing around you, or on words you need right now to be able to say something important ("eggs," "the Internet doesn't work," "I have a cold," etc.). Ideally, the dictionary needs to show accent marks, any shifting accents, case requirements (e.g. "сказáть что кому, о чём" or "через что, кого"), and word morphology: declensions (changing endings) for nouns, conjugations and aspect (perfective or imperfective) for verbs. This way you will be able to obtain answers to most questions you will have about words and their proper usage. These days good electronic dictionaries for portable electronic devices make this easier than ever. For instance, the excellent and voluminous Oxford English-Russian dictionary is now available as an application for the iPhone/iPod/iPad. There is also a decent "Slovoed" dictionary app including other major European languages as well.
If you follow these recommendations, making minor adjustments for your individual needs and learning style, I can guarantee that you will get over that initial learning hump within a few months, making your life in Ukraine that much easier and more multidimensional.