Moscow's metro system is not only one of the prettiest, but also one of the most efficient in the world. Trains are coming approximately every 1,5-2 minutes and bring you to your destination fast. It is quite clean compared to some other major city metro's and the routes are easy to understand. Especially with the app: "Yandex Metro" you can check the fastest routes and the projected time. Buy a "trojka card" and add money on it at the cash desk or at the machines. A one way trip is only 35 roubles, no matter how much you transfer or how far you go.
Nowadays most lines have both Russian and English communication on the trains and in the city center also most signage on the stations is in English. But if you know the alphabet you should be just fine and only pay attention to the direction of the train once you chose the color of you "line".
The opening hours are from 5.20 a.m. to 1.00 a.m. In rush hours (8.00-9.00, 17.00-19.00) the metro is overcrowded, so it's better to avoid.
Another way to travel in Moscow is with the mini-bus "marshrutka's".
These are small mini buses that drive to many destinations. Only use the blue ones with a sign as they are the official ones. If you see an approaching shuttle just wave it down like a taxi. You can pay with your trojka card on the bus (see metro) and it's 50RB one way. When you approach your stop just say to the driver where to stop. He will understand if you just say "Stop!" but it's better to say it in Russian «Ostanovite pozhaluista». Check out the schedule and expected time to destination with the "Yandex transport" app.
Taxi's are cheap in Moscow, but don't stop a random taxi on the street as they might be illegal and overcharging. We advice to use the "Gett taxi" or "Yandex taxi" app, because you can see the expected arrival times, route and rating of the drivers.