I being a Russian speaker completely agree with Marcus except that I think that inserting the "y" as advised in English textbooks is even more detrimental than he asserts.

My advise to English speakers: if you do not know how to pronounce the soft consonants, just ignore them, but do NOT insert that weird "y".

This is especially related to cases when the consosnant is followed with "е". It is very disappointing to me to occasionally see Russian words transliterated into English as " Byelorussia" instead of "Belorussia", "Lyudmila" instead of "Ludmila" so on. If you pronounce these words with hard consonant, it is nothing more than a minor accent difference. If you insert the "y", you get other words. With vowels "я" and "ё" the situation is more difficult though and just ignoring the softness is much worse here.

But if we recall the historic development we will see that they derived from "ea->я", "eo->ё", "еу->ю". For example the Russian name Фёдор is derived from Greek "Theodor". Thus is is much natural and better reflects the pronunciation to transliterate is as "Feodor" rather than "Fyodor". Think about these vowels as of short forms of the diphthongs. Pronounce "я" as "еа", "ё" as "ео", "ю" as "еу". Note that it is closer to German to English transliteration rules as well.

Take for example the surname of a Russian writer Беляев. I occasionaly see it transliterated as "Belyaev". This makes me funny because such change makes the family to look like it was derived from Russian word "бельё" ("belyo") which means "underwear". The surname then sounds like "Underwear-man". Similarly the Moscow metro station "Беляево" when transliterated as "Belyayevo" looks like an "Underwear-station". I suggest to better transliterate and pronounce the name as "Beleaev" or "Beleayev".