Russian is a difficult language. The grammar is complex... including tons of grammatical concepts that English doesn't have.
If you were to *live* in Russia and use it full-time, you could probably speak it poorly after three months, good in six months, and really well in a year.
The best single investment you can make is "How to Learn Any Language: Quickly, Easily, Inexpensively, Enjoyably and on Your Own" by Barry M. Farber. He speaks many languages fluently and says some things about learning languages that I have found to be right on the mark. It's an easy book to read and very entertaining. The most important things he says are:
1. Practice every day. You will need about 600 hours of study to really speak it well. If you do an hour a day it's two years.
2. Create flash cards and use them. While you're waiting in line at the bank, standing in the kitchen waiting for water to boil, during commercials on television. There are tons of minutes in a day that go to waste and flash cards are a great opportunity to mop up that time and use it productively.
3. Use a multi-pronged approach. Speak some with native speakers, study some from a grammar book, read newspapers, do audio courses, etc. all a little bit.
4. Try to make learning fun and interesting. If you just get a grammar book and study grammar all day you'll get bored.
His point about making it fun is important. Try to read a Russian newspaper, and make flash cards out of all the words you don't know. The very first paragraph will take a very long time. But, on the second paragraph, you'll already know a lot of the words because they also appeared in the first paragraph. This is fun because it is sort of like a puzzle and it is interesting to finally figure out what is being said in this real-world application of language.
My favorite Russian reading to do is to go over to the Russian womens' board and see what they're talking about. Super interesting!

If you're going to study on your own in the USA, plan on devoting at least an hour a day it...and don't skip any days. If you do this consistently, you can probably have a pretty good grasp of the language in a couple of years.
The best place to get started is Pimsleur. It's a series of audio courses available on tape or MP3. There's 90 half-hour lessons in all, and you'll need to do each one two or three times (unless you learn faster than me). If you can devote 60 to 90 minutes a day on this, you'll be speaking a significant amount of Russian in only three months. Pimsleur is a little expensive, though... if you buy all 90 lessons (three courses of 30 lessons each) at once, you can get them for around $600. However, if you're less than ethical, there are people on the internet that sell pirated versions of Pimsleur in mp3 format for about $25. Even if you pay the full price, Pimsleur is worth it. You'll be amazed with your progress. I had only done Pimsleur when I landed in Russia the first time and could get around OK, buy tickets, talk to the desk people at hotels, argue with the dumbass immigration people at the airport, etc.
Especially if your time is limited... doing the 90 days of Pimsleur will help you out a lot in Russia.
Pimsleur doesn't do a good job of teaching you to read or write, though. Pimsleur is a great place to start, but you'll need more.
I think the Rosetta Stone software is helpful, especially if you don't have a teacher. It's helpful for me to hear text being spoken at the same time I see it. The annoying thing about Rosetta Stone is that you have to look a lot of words up in the dictionary because there is no English. This is more and more true the farther into it you get. Some people don't like Rosetta stone because it's a little boring, but you can get around that by not doing it for long sessions. I often run it for twenty minutes before I go to work.
DON'T take a class. Classes are a waste of time. It is better to study on your own than take a class. Some people say that they won't be disciplined if they don't take a class. I think that if you don't have the discipline to do it without a class, you won't end up learning it with a class. Discipline is what will help you learn Russian.
However, individual instruction (as opposed to classes) is highly useful. The teacher I'm studying with now I met through one of these chat boards. I also occasionally see Russian teachers post on Craigslist. I also found a teacher by asking around in the Russian community. Don't just find a native speaker, though, it will be a waste of time. Find someone who has studied linguistics professionally and who has experience teaching Russian to foreigners.
I've been studying Russian for slightly over two years and I can talk about anything with people that are patient enough. I often don't know the word I want, but I can come up with a different way to describe what I'm trying to say. I understand the Russian noun cases pretty well and usually use them correctly. I have a vocabulary of between fifteen hundred and two thousand words. I have no problem speaking to Russian women on the phone.
Russian is really a beautiful language and it gets even more fascinating with time... but it is not a simple undertaking.
Learning Russian and how it will open doors. People are genuinely friendly when you try to speak their language--especially if it is an off-the-beaten-path language like Russian. By the way, the single most useful phrase you can learn is "Excuse me, I'm still learning to speak your beautiful language. Can you tell me ..." It can turn the most insolent jerk into your friend.
Nouns, in particular, are tricky. In English, you indicate the relationship between objects and subjects with the word order. In Russian, you have much more flexibility in the word order and change the noun endings to indicate relationships. If you try to describe a complex action "I gave Lena the letter from my pocket that had been written with the blue pen" in Russian and get the endings wrong, nobody will understand. ("Did he take the letter from Lena and put it in his pocket, or from his pocket and gave it to Lena? Did he give her the blue pen indicated in the letter, or a letter written with the blue pen?") What Fadamor says about accents in questions is right on, especially if you do not use a question word. I still can't do this right and always confuse Russians--they don't know if I'm making a statement or asking a question.
I think that learning the language is an excellent idea. Some guys go after only English-speaking women, but it seems to me that finding an English-speaking girl is not enough. Since most of us aren't going to go live with our potential spouses for months on end, we need to learn a lot about them in a hurry in order to make a decision. I think that one of the best ways to learn a lot about someone is to develop a good relationship with their family members and friends. You can learn a lot about someone by getting to know their parents and see what kinds of friends they choose. Even if the lady you find speaks English, you can pick up on so many subtle things if you can understand some Russian.