Personally, I transliterate "И" as "I" and "Ы" as "Y" (I don't know how common this practise is, it's definitely not universal). It gets a bit messy with words that end in "Й," unfortunately... I used to transliterate "ИЙ" as "IJ" and "ЫЙ" as "YJ," as that is how it is done in Czech, but that, I found, is extremely confusing to anyone unfamiliar with Eastern European spelling practises (those same people constantly vex me with their stubborn inability to pronounce my surname, unless they are aficionados of classical music), so I started leaving the "J" out.
Speaking of which, if you think foreigners have trouble with "Ы," try explaining the difference between "Ш" and "Щ." Or better yet, the very idea of "Ь" and "Ъ."
"Ш" and "Щ" - I won't even try to explain:)
Thank you!
I've always explained it as "Ш is a gentle whisper, Щ is a bit harsher yet still a softer sound than Ч, as though the first is a breeze blowing in your ear, the second is rustling leaves, and the third is a twig snapping underneath your foot." I think the subtlety is lost on most people, sadly...