The largest country in the world, the sun can be rising in on one side of Russia as it sets on the other. I have traveled across nine timezones in Russia, overland. Thanks to Russia's reliable train system, this is a relatively easy and comfortable process.
In a country this big, there is a bit of everything. Some places are hilly, even mountainous. Others are flat, for miles around you. There are big cities and small villages, lots of different ethnic groups, great poverty and great wealth - and much more.
I have seen people go to Russia knowing no Russian at all and surviving. However, it's nice to be able to do a little more than just survive, and you'll certainly have an easier time if you learn some basic Russian.
One of the most important - and straightforward - things to learn is the Russian alphabet. Street signs are rarely transliterated into the Latin alphabet, and there are even some words you can work out just by knowing what the Russian sounds like. The lowercase letters are in almost all cases just the uppercase ones but smaller, which makes things easier still. I really can't recommend strongly enough learning at least to read the alphabet.
If you want to be able to walk into just about any restaurant and not care whether they have a menu in English (if you're heading anywhere but the largest cities, it will be the case in most restaurants), learn some food words. You don't need much: my vocabulary was beef, chicken, pork, fish, onion, potato, coffee, tea, milk and beer at the start of my journey, and hadn't improved all that much by the end. It was enough for me to be able to choose something that I would like in pretty much every place I went though (and avoid fish, which I don't like).
Speaking and listening is next up. Obviously, the common things (please, thank you, hello, goodbye) are good to know. Some numbers can be good too, and if you want to tell people a little about yourself then knowing how to say what country you are from, what your name is and what your job is will at least show them you've made some effort. Being able to talk about your trip makes a talking point - the easiest way is to have a map and point out the places, though. ;-)
I used the Pimsleur Audio Russian lessons, and found that they gave me a some useful vocabulary and some confidence. If you do have the time to invest in learning the language, they may work well for you, but everyone's different. They come with reading lessons too, to teach you the alphabet. I learned it from there.
Perhaps the most annoying part of visiting Russia is obtaining the visa (a process that, if you have money to throw at it, can still be straightforward). My experience so far has been that, beyond that point, things are fairly straightforward. At the points of entry and exit, I've had no problems to date.
It is important to make sure you get your visa registered after you arrive, or you could create yourself some problems on exit. One escape from this can be to exit Russia to Belarus. It's an even more challenging country to visit in some senses, but they do for many people visa on arrival, and when you leave Belarus they'll only care that you registered in Belarus. Do not rely on this, and of course I totally didn't use this to get away with losing some paperwork on a train. ;-)
It is best to try and avoid run-ins with the authorities, as they're known for being potentially unpleasant. That said, I haven't found it hard to avoid their attention. Then, I didn't wonder the streets completely drunk or otherwise draw attention to myself either. Exercise some common sense.
You are meant to carry ID all of the time. Which is fine, but you'll often also have to leave your passport at the hotel for registration. I'd advise taking a photocopy of your passport out with you in these cases, and if your hotel gives you a guest card take that.
