Most international flights arrive at Terminal 2 or the new Terminal C at Sheremetyevo Airport (Airport code SVO - 24 miles or 39 km north west of the city) or Domodedovo Airport (Airport code DME - 22 miles or 35 km south of the city). Many major hotels have transfers from and to the airports. Official yellow cabs are readily available. There are private cars for hire on the spot at the airports, but those should be avoided if you travel alone, and the price should be settled in advance.  A good option can be to arrange for a private car through one of the many online travel services or Apartment rental business that serve Moscow travelers.  Most private cars will generally be more expensive than an official airport taxi, but they have the advantage of a person with your name on a piece of paper meeting you and there is no need to worry about getting a taxi and trying to explain where you are going.

Traveling to/from the city center and the airports by car is often a time-consuming enterprise in Moscow.  Moscow traffic is very heavy and huge traffic jams are a daily event - especially, it seems, on the two main routes to the two main international airports.  If you do use car to travel to either airport, you are well advised during any normal hours of the day or evening (from 9:00am to 9:00pm in reality) to allow 2 hours to reach the airport.  The time may be less than that, but as the incidence of traffic jams is high and highly unpredictable, the extra time is needed to ensure you arrive at the airport on time.  During other times when the roads are quiet, the trip to either airport will take about 45 minutes (from the City Centre).  Public transportation is available to both airports, but for now, the public transport options to Sheremetyevo are not as attractive and easy to use as those to Domodedovo.  A summary of each follows:

Domodedovo: For traveling to/from Domodedovo and the city center, you can take an airport express train (creatively named the "AeroExpress") which travels regularly between the airport and the Paveletsky train station.  If you can do it, this is definitely the best way to travel to/from Domodedovo.  The highway between the city and Domodedovo is almost always full of traffic jams, unless you are traveling during the wee hours of the morning, or any time before, say, 9:00 am on a weekend.  Adjacent to the Paveletsky station is the Paveletskaya Metro station, so you can easily connect from the train to the Metro, which will take you all over the city.  See "Metro"below.

Sheremetyevo: To travel, by public transport,  between Sheremetyevo Terminal 2 (which is the main international terminal at SVO) and the city, you may take a bus, taxi or marshrutka (mini-bus that operates along a pre-defined route) between the airport and the Rechnoy Vokzal metro station.  Once you reach the metro station from the airport, you can then travel by Metro into the city center, thus avoiding the frequent traffic jams along the way.  See "Metro" below.  Of course, there's no guarantee that your bus, taxi or marshrutka won't get stuck in traffic between the airport and Rechnoy Vokzal, so when heading from the city to the airport, allow plenty of time.  A better option may be the AeroExpress train that travels between Savelovsky Train Station (which is adjacent to Savelovskaya Metro Station) to the Lobnaya station near Sheremetyevo.  Between Lobnaya and Sheremetyevo, you can take one of the white busses labeled "Sheremetevo 1-2, Lobnaya."  The busses serve both SVO Terminal 1/C and SVO Terminal 2.  Beginning in 2008, plans call for train service direct from the Belorussky  train station (Adjacent to the Belorusskaya Metro Station, not far from the city center) to the new (still under construction, as of March '08) train terminal at SVO terminal 2.  The most recently-published estimate calls for completion of this rail route sometime in July 2008.

Terminal Transfers at SVO: Also note that getting from SVO terminal 1/C to SVO terminal 2 is not a simple matter of walking or taking a moving sidewalk, like it is at many international airports.  The two terminals are on opposite sides of the runways from each other, and the only way to get from one to the other is by vehicle which will drive you around the airport, taking 10 to 15 minutes on a good traffic day.  Of course, there are taxi drivers who will drive you between the terminals, but they have been known to charge outrageous fees for that short ride (some say as much as $100).  There are also busses which make the trip between the terminals on a regular basis, and for a much more reasonable fee.  Inquire at the information desk.  If you are arriving at SVO terminal 2 and transferring to a Russian domestic flight which leaves out of terminal 1, check with your travel agent or airline to see if there is a pre-arranged transfer between terminals.  If you have an extended delay between your international flight and your domestic flight, it is far better to stay at Terminal 2 as long as possible, as the facilities there are far superior than at Terminal 1 (using the new Termincal C located next to Terminal 1 is also an option, as they have good, and new, facilities).

Immigration and Customs: Clearing the immigration/passport control checkpoint at either airport can be a long, frustrating experience.  After disembarking from your plane, the first thing you must do is get in line for the passport control officer.  If you are a foreigner, you should have been given an entry card to fill out on the plane prior to arrival.  If you do not receive such a form, ask the flight attendant for one.  If the flight crew doesn't have any (which sometimes happens) then you will need to get one in the arrivals hall and fill it out there.  A good idea in this case is to pick up two forms (one extra, in case you need it) and then go stand in line at passport control while you fill it out.  The form has two halves, each requesting identical information.  You must fill in both halves, as one will be kept by the passport control officer, and the other will be stamped and returned to you, to show that you entered Russia legally.  If there are lots of arrivals at the same time you arrive, you can expect a fairly long wait at passport control.  Waits of 2 hours are not unheard of, although that is rare.  Waits of 30 minutes to an hour are more common.  Sometimes, however, you can simply walk right up and get through passport control in 10 minutes or less.  It all just depends on how many flights have arrived, and how many immigration officers are on duty at the time.  Typically, the only questions/comments from the passport control officer are "Where are you coming from?", and "Please remove your sunglasses, hat, etc."  (So they can clearly see your face and compare to your passport).  Often, they say nothing at all - especially to foreigners.  There are different lines for foreigner and Russian passport holders - at Sheremetyevo they are in the same hall (left side for Russians and right side for foreigners) and at Domodedovo as you approach immigration to the left side is the hall for foreigners and the right side is for Russians.

Once you clear passport control, you will enter the baggage claim area.  If your trip through passport control was quick, you will likely have to wait a bit for your bags, but if the passport control line is more typical, your bags will likely be waiting on you.  If your bags don't arrive, the lost baggage desk is located in the baggage claim hall.  Lost baggage does not seem to be any greater problem arriving in Moscow, than anywhere else.  Sometimes it happens, but usually not - it really depends more on the airline and your connecting flights than anything else.  After claiming your bags, you can proceed past the customs checkpoint.  If you have nothing to declare, proceed through the green line, where you may be asked to scan your bags through an x-ray machine, but quite often you will not be stopped at all.  Of course, customs can hand-inspect your bags as well, but this is even more rare, and, like most places, usually only occurs if they have reason to suspect something.  You can check customs import restrictions here to see what the limits are, without declaring anything.  If you have something to declare, be prepared for some paperwork, and depending on what it is, you may have to pay an import duty of as much as 30%.  For alcohol, you are allowed to bring in two liters, without declaration.  Wine bottles are .75 liters, but they will typically allow you to bring in three bottles of wine without a problem, even though it is slightly over 2 liters.  After you have cleared customs, you will enter the arrivals hall of the terminal building and then it's off to the city on your chosen mode of transport, per the descriptions above.

Metro: Be advised that the Metro generally doesn't have signs and instructions in English, so if you don't read Russian, you will be well-advised to study the Metro map in advance of your arrival, just to get a feel for how it is laid out, and the locations of the stations that you need.  It would also be wise to carry a pocket-size metro map with you, in both Russian and English.  It is generally much easier to use a Russian language map as you can much more easily identify the words on the map with the words on the signs in the metro, but best of all is a map that has both Russian and English.  You can find many printable versions of these online.  You need to buy metro tickets before entering the metro and there are cashiers at every metro station.  See TripAdvisor Inside Pages item called "How to Use the Metro." 

Traveling to Moscow by Train: Trains can be cheaper than flying and run from many European cities. Moscow train stations are located near the city center and subway stations.