Learn a few Russian phrases ahead of time or else cab drivers will rip you off.
You may be quite proud of learning to ask "Do you speak English?" in Russian, but this phrase is useless at the airport. Opening a conversation this way signals that you can be "taken for a ride." The next thing you know, you've paid $100 USD in cab fare to get to the center of the city — a trip that usually costs about $25 USD.
Instead, learn phrases like "What's your name?" and "Where are you from?" It will help a lot to be able to count to ten if you want to try any sort of negotiation. Duolingo has an excellent Russian course that's completely free.
Demonstrating even limited abilities with the Russian language will go a long way toward getting you a fair shake in Moscow.