Looks like you're from across that ocean. Well, first you have to add cyrillic support in your OS. I suppose it's Windows XP you're using. Go to Control panel > Regional and Language Options > Languages > Details > select ADD and add whatever you want (Russian in this case) Answer Yes to whatever it asks and Reboot.
What you do next depends of what kind of fonts you want to use. If you want Type 1 you have to find those with cyrillic characters to make use of that. If you're thinking about TTF or OTF, your problem has been basically solved because a lot of that already comes with the system, and now Illustrator is going to group font names in groups with just Western support, Cyrillic, etc., and all you have to do is select the right own. I am sure you know just what TTFs and OTFs and Type1 have cyrillic table.
That's about it. I hope I guessed right and this is helpful.