A student in Russia needs $200-250 per month on average or $2000-2500 per academic year (September to June). It's better to bring about $200-300 with you for extra expenses like medical insurance, living arrangements in an apartment or dormitory (buying dishes, bed linen and detergents), and to purchase some books.
Dormitory – 1449 rubles (~$20)
Food – 7 587 rubles (~$100)
Transport – 1 270 rubles (~$16)
Internet, mobile services – 800 rubles (~$11)
Cultural, sport and other activities – 4000 rubles (~$57)
TOTAL: 15 157 rubles (~$200).