In Russia taxis are mafia controlled and can be expensive in Moscow and Saint Petersburg. Be sure to discuss the price before getting in and don't get in a taxi with other people in it, unless they are tourists also. Try to share the ride with people you meet on the plane if possible. Never get out of the taxi before the driver if you have bags in the trunk. Never pay the driver before you have your bags out of the trunk. Have exact change, because they never seem to be able to make change for you. You can also hail a private car (hitch hiking), just stick your arm straight from your body towards the road, and with in seconds a car will stop. Of course it helps to speak a little Russian, or at least have a map and point to where you want to go, the driver will tell you how much, you can haggle with him until you both agree on a price. But this is risky, and I wouldn't suggest doing this. I suggest looking for a private taxi.

If at all possible avoid taxis and take the Metro. Russia now has mini van buses that seat about 11-13 people and they only fill with people the number of seats available, cost is about two times more than the bus but much more comfortable with less stops. I suggest using them. All buses, and mini vans are numbered, so once you know the number of the bus or mini van that gets you to where you going, it will also be the same one that gets you back to where you came from. Children under 5 are free on all public transportation.