Here's what I do. First, one needs to recognize that to the following must all be acquired if you want to gain and retain for the long run a truly useful set of language skills:
- reading skills: being able to read signs, basic instructions, etc.
- listening comprehension: understanding much of what natives say when talking at normal speed
- speaking skills, including decent pronunciation (even if you speak very slowly)
- familiarity with all the basic grammar concepts
Most importantly, you'll need a high-quality language course that includes the following:
- lessons incorporating not much less or much more than 1500 words, including the most commonly used and useful words of the language
- explanations of all basic grammar principles of the language that don't go into excessive detail
- at least 1 hour of audio material including complete sentences, preferably conversations and texts, spoken at near-normal speed by natives and including all vocabulary words in the course
Unfortunately, Langenscheidt's Russian course is available only in German! In Ukraine you can find many Langenscheidt course books translated into Russian or Ukrainian -- German, Spanish, French, Polish, and others. I've used a couple of these with great success and recommend them highly.
If you don't speak German, you'll need to find something similar to the Langenscheidt course with all the features I've mentioned. It shouldn't have to cost much more than $30 USD. Surely there must be some similarly structured courses out there.
How to use a language course for self-learners
If you know how to utilize courses like Langenscheidt's to your advantage, there is simply no need to pay for expensive, high-tech, newfangled language learning methodologies (I won't name names). My opinion is that such courses are for people with learning difficulties or for those who simply don't know any better. Sorry if I offended anyone!
When I use a Langenscheidt course, I start by working through the texts of the first several lessons and figuring out what they are saying. (With Russian/Ukrainian there will be the initial difficulty of learning the alphabet first, which will slow you down for a while.) I pay attention to the grammar notes and use them to help figure out the text. I don't try to memorize anything, but sometimes I make lists of conjugations or important word sets -- for instance, "I - my - mine, you - your - yours, he - his - his, she - her - hers, it - its - its, we - our - ours, you - your - yours, they - their - theirs." I basically skip the exercises till a later date when I've built up my familiarity with the sounds and the forms. Some people like exercises and are comfortable doing them from the outset.
Then, I start listening to the audio. It's important to spend at least as much time listening to the audio recordings as you do working with the textbook. Your brain needs time to digest the new sounds and learn to differentiate words from the stream of sounds. I might go through 3 lessons of the textbook, then listen to the audio for the lessons one time through without looking at the book, to see what I am able to recognize from the text. Then I might listen to the recordings a few more times while looking at the text, to see if I can pick up more of it. Finally, I'll listen to the recordings again without looking at the texts. The goal is in the end to be able to listen to all the audio for the course and understand all of it without consulting the textbook. Too often, language learners fail to focus on listening comprehension. But if you don't, you'll never get the pronunciation right and you won't understand it when people use the words that you have supposedly already learned.
The nice thing about listening is that you can do it while doing other things -- driving, jogging, walking, cleaning, etc. You don't have to understand everything for it to be useful. Generally, each time you listen to a recording you'll pick up a bit of new information whether you realize it or not.
It's important to avoid stressing while learning a foreign language (or anything else, for that matter). Stress means that much of your mental energy is being wasted as "heat" instead of being used for a useful purpose. If learning a foreign language is stressing you, there might be something more basic that you don't understand that is preventing you from understanding the new material. For this reason it is useful to study a very simple language such as Esperanto before attacking real foreign languages. Studies show that students who spent a year learning Esperanto before subsequently learning French did a lot better than those who spent the whole time learning just French (see link). Learning Esperanto first familiarized them with the basic structure of languages in general, and after that it was easier to apply what they had learned to a natural and more difficult language.
As an example of avoiding stress, I personally don't like doing exercises -- conjugating verbs, practicing declensions, translating texts, etc. So I just skip them! My focus is on learning how to say the important things I need to say. Exercises are nothing more than a tool to help achieve this, and they don't work for everyone.
Find a native -- if you can
At some point in your language learning, it can be very beneficial to meet with a native speaker to ask if you're saying things correctly and to learn some additional phrases and vocabulary that you expect to need. Language clubs -- if they exist in your city or town -- are a great way to get this added exposure.
Q&A
Feel free to post questions regarding learning Russian and Ukrainian effectively on your own. Also, if anyone knows of do-it-yourself language courses like what I've described here, please post information so that others can find them.
UPDATE 2016:
I have finally decided to teach others my method for learning and mastering foreign languages at www.FrictionlessMastery.com. Take a look and download or order my book and/or instruction manual. My views and methods have are clearer and more evolved than what I wrote here.