two different approaches possible. first is something like letter-to-letter transcript, but you need to know how to pronounce correctly, second one is transcript which pronounced in english will sound almost identical as in original.
example: ИЛЬИНОВ Евгений
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Evgenij (in east europe)- probably Evgenii in english
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Yevgeniy - pronounced in english very close to russian pronounciation
so both ways are somehow correct.
it is getting more complicated in surname.
И is letter "i", but pronounced in russian like "e" in english, so:
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Ilinov
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Elyinov
but you can find also Ilyionov. which is both methods mixed together. bit of a mess..