Public transport in Russia (especially Moscow in my experience) is excellent.
The Metro system would have to be up there among the best in the world in terms of ease of use and beauty. It contains twelve lines with a total of 177 stations. The Metro is one of world's busiest serving more than nine million passengers daily.
While the general feel of the Metro may put some people off I can't praise it highly enough. It is fast, efficient, cheap and safe and all of the platforms are works of art in themselves. In the last year I have experienced the metro systems of Moscow, London, Helsinki and now in Tokyo and I would rate the Moscow metro better overall then any of them, sure the others have some obvious good points but as a package The Metro can't be beat.
If for no other reason, check out the Metro to take in the stations, especially those on the Red (original) line. You won't be disappointed. Two of the most interesting stations are Komsomolskaya and Novoslobodskaya. The latter is deep and was used as a makeshift assembly hall for a Party meeting marking the anniversary of the Revolution during the Nazi bombardments in the winter of 1941. You can buy a ticket and get on and off the train at each station as long as you don't go out of the station you are free to ride to where ever you want.
The metro is open from 6am to 1am. The trains run every 2-3 minutes from every station MAX so you are never waiting for long. In the 6 months we lived in Moscow earlier this year, I never experienced stoppages, delays, slow trains or anything of the sort (which we had to put up with all the time over a week of using the London Underground).
Moscow Metro Site: http://engl.mosmetro.ru/
There is a single price ticket structure so doesn't matter if you are going 1 station or from 1 end of the metro to the other it is the same price. Generally, ticket queues are short as it is a simple pricing structure so people are just buying a set amount of tickets not working out how much it is going to cost them to get from A to B.
A single trip costs 22 rubles with tickets sold at manned booths within the stations (kassa). There are a few stations with tickets vending machines.
A multi-trip card for 10 or 20 trips (10 at 200 rubles) can make travel even easier. There is also an unlimited monthly pass that runs by calendar month. For more information on tickets and prices, go to the official Metro site's price list.
I don't know much about long distance train travel, but believe like most things in Russia it will be highly efficient if not overly comfortable. Moscow is the western terminus of the Trans-Siberian Railway, which covers nearly 9,300 kilometres (5,779 mi) of Russian territory to Vladivostok on the Pacific coast.
Russian Train Site: http://www.poezda.net/en/index
The bus system, while reasonably efficient, can be subject to traffic issues. It is sometimes a case of having to know when it is more efficient to actually jump off the bus and walk to your next stop. Once you master that skill they are still a cheap and efficient means of transport.
Fares are comparable with kupeny (2nd-class) train fares. To buy domestic tickets, go to Moscow's long-distance bus terminal, the Shchyolkovsky bus station.
In tandem with the public buses, there are some private mini-buses. A cheap and efficient way of getting around, but you are taking your safety into your own hands the moment you step into one of these. They are pretty much unregulated (hence the reason to try and make them illegal) and are often dodgy as hell. Sometimes you can be jammed in like sardines and if you are unfamiliar with where you are going or the Russian language you are best to avoid these.
Taxis in Moscow can be expensive as traffic is so bad you can spend hours just sitting. Unless you know it is a good traffic day, I'd stick to public transport.
Official taxis may be recognized by their checkerboard logo on the side and/or a small green light in the windscreen. If you book a taxi over the phone (hotel staff will do this for you if you don't speak Russian), the dispatcher will normally ring back within a few minutes to provide a description and license number of the car. It's best to provide at least an hour's notice before you need the taxi. Note that unofficial cabs are also acceptable and it is common everyday drivers to pick up people hailing a cab.
Most destinations should be reachable within the Garden Ring for 200 rubles or less, unless it's a high time (national holiday or hours when metro is not running).
Moscow Taxi companies:
By Tony Fitzpatrick, a kiwi businessman who traded a solar powered life in the country with no neighbours for a fourth floor apartment in Moscow. Follow his exploits in their move to Japan on: