I will be leaving for my second trip to Russia three weeks from today. While that definately doesn't make me an expert I will tell you about the things I picked up the first time in case it helps. It will be a little long winded but I will give you the information I wish I had had the first time. Especially for the flights because that was the most akward part for me.
Spoiler warning: Some of this might spoil the adventure of discovery for you so if you are worried about that just kind of skim what I am saying and read the parts you want to know about.
First thing is that once you get to Sheremetyevo airport just kind of follow the crowd to the immigration/customs control booth. The area is clearly marked so it won't be too hard once you get there to figure out what line to get in. Once they verify your visa is correct, you will pick up your luggage and go through customs. Again, a pretty easy (and surprisingly fast) process.
Immediately after you get through customs you enter the main part of the terminal. Be prepared to be literally assaulted by cab drivers. I mean it they will horde on you like the Rooks during an RJO. They will try to grab your luggage, try to convince you to ride with them, etc. I do not know how true it is but from everything I have read and heard from both Russans and foreigners do NOT accept a ride from any of them. Instead either take public transportation or pre-arrange a trustworthy driver to meet you.
When I was there I had pre-arranged for a driver named Slava. He spoke understandable English and was as much a tour guide as a driver. His car was also clean and he drove safely. I really also really enjoyed his stories. He charges a flat rate (plus tip of course) of $40 to the center of Moscow or $30 to transfer airports. If you are interested in contacting him he can be reached through his web site at
http://www.moscowdrivers.net/index.php. The domestic flights are a little different too. I flew out of the Sheremetyevo domestic terminal which may be different then the one you are going to use but I will tell you what it and the airport in Volgograd were like.
The security pre-screen is much like here in the states but once you get through there you check in at what reminds me of a ticket counter. Check-in will take place at a row of booths with one booth for each flight. There they will assign your seat and check your luggage. Then you go sit in the lounge. When they call your flight you will move to the door and then wait outside. A bus will pull up and you will eventually get on it to be taken to the plane. While seats are assigned on the plane, there will still be the mad scramble to get on to the plane. It is rather chaotic so be prepared to be jostled and bumped.
Again, the Volgograd airport might be different then where you are going, but at the Volgograd airport you ride us a bus to a gate in the fence. You go through there and the luggage collection area was in what looked like a small warehouse to me. Collect your bags from there and then start looking for transportation to your hotel. Cab coverage can be pretty intermittent so be prepared to either pre-arrange a ride (most hotels offer this) or to take public transportation.
A few other tips I would give you would be to arrange for some type of translator. A person to accompany would be best, but if that is not in the plan then look into getting some kind of book or electronic gizmo. I personally loaded a Russian-English-Russian dictionary onto my Palm PC and it helped ALOT. Ectaco makes some pretty decent software.
I woild also suggest that you take a good mix of cash, traveler's checks, and plastic with you to cover your expenses. Most cities outside of Moscow and St. Petersburg do not accept dollars. You can however exchange travellers checks and cash at most banks though they will charge you a commision. Also, outside of some banks there are "private" money exchangers who will generally give you a better deal then the bank. Credit cards will most of the time not be accepted in restaurants and the like outside of Moscow and St. Petersburg but I did find a bit of a loophole. I have one of those Credit/Debit cards. In Volgograd there are ATMs everywhere. Since hitting an ATM was far easier then going through all the hassle of exchanging money at a bank I used them to get money for most of my expenses. The loophole was that, unlike the banks, the ATMs did NOT appear to charge any commision on the money I took out. They also appeared to be a bit more generous then the banks on the exchange rate. Be prepared to eat (a lot) and expect each meal to take quite a long time as they are all multi-course and each course comes in its own time.
Final thing I can think of is culture related. Russians do not smile or make eye-contact as much as Westerners. Do not be alarmed by this just letting you know since it caught me off guard. Also, respect the crosswalks and walk/don't walk lights. As soon as a traffic light turns green the drivers will go and if you happen to be in their way too bad for you. Finally, be sure to have your passport on you at all times and to carry all your valuables in a front pocket or someplace safe like that.
I can think of a million other things but I don't want to take all the fun away. If you can think of any other things you might want to know just ask and I will try to answer your questions as best I can.
Just remember to be polite to people and aware and you will have a great time. Russians are some of the best people in the world.