Learn some of the Cyrillic alphabet and language before you leave for Moscow. Although this isn't a definite requirement to learn how to navigate the Moscow metro, it will certainly be a help.
Exchange your money for rubles and be sure you have exact change to purchase the tickets you will need to ride the Moscow metro--the babushki hate big bills.
Buy a ticket for the Moscow metro. You can get 10 ride tickets for 125 rubles. Each ride is one ticket. You will need to know how to say "ten please"--"deeset pajolsta."
Feed the ticket into the entry gate. The ticket should be arrow side down when you put it into the slot. You put it in and pull it out and a green light should come on until you pass through.
Read the overhead signs to find the correct Moscow metro line. Once you find the one you want, take the escalator down to the metro lines. When you arrive at the bottom, you will need to check the overhead signs again to find out which side of the platform you need to be on for your train.
Transfer to other lines. If you need to connect to other lines, you should follow the overhead signs. Everything is clearly marked and should be easy to find.