For general information on getting around Moscow, you can check out the relevant sections of guides such as WikiVoyage, where information is generally up to date. Useful information about Moscow can also be found at the Wikitravel page.
Moscow is currently served by four international airports, of which you are likely to arrive at three: Sheremetyevo (SVO), Domodedovo (DME) and Vnukovo (VKO). All three are connected to the city centre by Aeroexpress trains, which is the most convenient method, as it allows you to avoid heavy traffic that is typical of the main roads leading into Moscow. At all airports you will find signs showing the way to the train station. Tickets can be bought at the airport at ticket machines (which accept all international credit cards) or at ticket booths. The cost of the ticket is 500 RUB. Travel time depends on the airport and takes from 30 to 47 minutes.
Aeroexpress trains terminate at one of the main central railway stations: Belorusskaya for SVO, Paveletskaya for DME, and Kievskaya for VKO. All these stations have connected metro stops, and you should be able to reach any of the hotels within 20-30 minutes of travel.
Taking a taxi to the city centre may cause delays, as heavy traffic, especially on weekdays, can make the trip unpredictable. If you decide to hire a taxi, avoid the services of the drivers who approach you at the airport. These prey off unsuspecting tourists and their prices can be as high as 10 times the normal amount. Instead of this, you can choose one of two options:
Use one of the taxi rental services (Uber, Gett, Yandex.Taxi), information on which can be found below. Prices for airport trips range from about 750 to about 1500 RUB depending on time, car, destination, etc.
Moscow is served by an extensive network of public transport, of which the largest and most convenient is the metro. Metro lines connect most parts of the city; in the centre, their density is such that you hardly need any other means of transport. Metro stations are open from 5:30 AM till 1:00 AM, and trains circulate with intervals ranging from around 5 minutes during offpeak hours to around 2.5 minutes or less during the day.
The official plan of the metro can be downloaded here.
A convenient way to plan your metro trips is Yandex.Metro (also available as an Android/iPhone app), which can calculate the shortest trips between any two stations, also showing approximate travel time.
All metro announcements are now translated into English. All stations and metro cars have plans of the metro inside, and at some stations, interactive maps with integrated route planners are also available.
A new addition to the transport system of Moscow is the Moscow Central Circle, which is an urban railroad (similar to S-Bahn or RER). Some stations have direct connections to the metro, but in most cases you have to walk between the two. This mode of transport is only useful if you are making long-distance trips around Moscow for commuting etc.; it should not be needed if you are staying in one of the central hotels.
Buses, trams and trolleybuses are generally less reliable than the metro due to unpredictable traffic. If you need to plan a bus trip, you can use the Yandex.Transport app (also available as a layer on Yandex.Maps), which shows transport circulation in real-time through GPS, and also displays approximate time till the next bus.
Moscow has unified tickets for all public transport. The most convenient way to travel is to use the Troika card, which is a transport card similar to London’s Oyster, Paris’ Navigo, etc. The card can be bought at any metro ticket booth for 50 RUB (the money will be returned to you if you decide to give it back). Afterwards you can put money on it either at ticket offices or at automated ticket machines. Both ticket offices and machines now accept banking cards. The price of a single trip using the Troika on any transport is 38 RUB. If you change from bus to metro or vice versa within 90 minutes, you will be charged 59 RUB for the whole trip.
You can also buy tickets for a fixed number of trips, but this is only cheaper if you buy a ticket for 60 trips. Day passes do not really pay off unless you do a lot of travel during the whole day. If you happen to travel on a bus without having bought a ticket in advance, you can buy one from the driver, for a larger than average price.
Taxi travel in Moscow is relatively affordable if you use one of the popular car rental services: Uber, Yandex.Taxi
There are also several English-speaking services available, but their fares are considerably higher than those of the ordinary companies.