You can (and you should, unless you have friends meeting you) arrange your transportation from the airport to the hotel in advance. There are many reputable services for that. You will give them your name and your flight number, and the driver will be waiting for you as you get through the passport control, holding out a sign with your name.
Every foreign passenger who gets off a plane in Sheremetyevo-2, the Moscow international airport, is immediately attacked by a hungry pack of car drivers offering their services in a rather aggressive way. Never use those. They are referred to as “taxi mafia,” and for a good reason. The way to deal with them is to firmly say “NO” (nyet in Russian) and to keep going, ignoring them from that point and looking for your driver. They still won’t leave you alone, of course; they will follow and continue to talk to you, but at least they will see that you are not even considering taking their car. When you find your driver, they will give up and let you go.
Moscow has a well-developed public transportation system, there are many buses and, of course, the famous Moscow “metro” – the subway. If you can read Cyrillic enough to understand maps, you should be able to get around on your own. Catching a cab is easy, but not recommended without being accompanied by a native Russian: the drivers will double or triple the price as soon as they see that you are a foreigner – and yes, I mean they will actually “see” it, even before you open your mouth and let them hear your accent. (It is not just the drivers’ thing, all Russians will take one look at you and know that you are a foreigner, no matter how hard you try to blend in and pretend to be one of them. I’m just saying it so that you know, and either wouldn’t try at all or wouldn’t get too upset when you fail.)
If you can’t read Cyrillic, you can hire an interpreter to explore the city with you, or use a reputable taxi service.