I stayed there for a summer as an exchange student in 1993. I think the most important thing to do is prepare for the culture shock. The division between rich and poor is huge in Russia and you will be a rich person, especially if you are paid in US Dollars. The exchange rate at the time fluctuated daily, and it will probably be smart not to convert all of your money to rubles at once. Try to get the most recent account you can of this.
At the time, my host mother paid the equivalent of $36USD for her 2 bedroom apartment in St. Petersburg. She lived in the Primorskaya region which is more modern, but had a lot of plumbing problems. Most of the regions are built in different specific eras. I liked the Smolenskaya region the best as it was near more actual culture and the apartments there I saw were nicer, albeit smaller. Older builldings may have communal kitchens and bathrooms, so watch out for that.
The first thing you will want when you get there is a metro pass, which can get you all over the city fast. It also prevents you from having to stamp tickets if you get a bus or tram. At the time it cost just under $1USD
Almost all the people I met were very friendly and supportive of each other. People tend to drink fairly heavily and it's common to have vodka shots after a meal. Beware some vodkas that are cheap and sold in the street are sometimes only partially vodka and are not safe to drink.
Also, I was surprised, but most host families appreciated American cigarettes as a gift. Smoking is everywhere there, and can be tough to get used to.
Most of the Russian men I spoke to were remarkably well read and enjoyed arguing politics. I never really understood why this was the case, but it's a definite cultural difference. A lot more people played chess there than I was used to seeing too, so it might be good to learn how.
I loved the time I spent there and wish I could go back. If you want to know more IM me.