Perhaps the most important point for the visitor is to note the difference between the way Russians treat people they are friends with, and those they deal with in passing (particularly officialdom).
Russians trust their friends and tend to be very loyal to them, and will extend this to friends of their friends too, especially if that means a visiting foreigner. They are far more likely than most Europeans, for example, to invite an acquaintance home, or have a drink with them, or help them out in some way.
The obverse of this is that they can be a lot more direct (or just bloody rude), and inconsiderate, to someone who is not connected to them, especially in Moscow and the big cities. This particularly applies to the people travellers have to deal with – hotel staff, train-ticket sellers, shop staff, bus drivers, and (God help you) the cops.
Foreigners are generally spared the worst of this kind of thing, but not always, by a long shot. Sometimes it’s hard to believe that they are the same race of people as the kind people you know personally. It’s all to do with years of having to deal with a state that sometimes seems to be committed to making life as hard as possible for its own people.
Outside the big cities, a lot of Russians don’t have much experience of foreigners. One old man told me the only people he’d ever met from abroad had been trying to kill him during world war two!
A lot also depends on who you are – or rather, where you come from. Russians very commonly cling to national stereotypes, and often have a fairly Darwinian view of different races. They have a lot of respect for the British, for example (because they were a big imperial power, like Russia), and the Germans (efficient, make good cars). People with dark skin are often looked down on. The ones who really cop it are the folk from the Caucasus, like Georgians, Armenians, and most of all, Chechens – travel in the Moscow metro, and you are pretty likely to see the police stopping such people for ID checks. This is mostly due to inherent racism rather than security concerns.
On the language side, not that many people speak English, though you are more likely to find younger people who can, than older ones. The situation is easier in big cities.