For a speaker of American English, the closest approximation in my opinion is "sheen lean." Of course, someone who doesn't speak American English minght not pronounce "sheen lean" the way I do.
The "hs" sound is difficult for many native English speakers to pronounce correctly. The sound is sort of half-way between the English "s" and "sh."
The letter "i" is most definitely pronounced like the English "long E."
By the way, "hsin" is the spelling used in the old Wade-Giles phonetic system. The modern "pinyin" equivalent would be "xin." But this won't help you pronounce it unless you happen to know the pinyin system.
If you really want to hear how it's pronounced, go to the link below and paste the following in the "Chinese to English" field:
心林
If you can't past the chiense characters in, try pasting into the second field "xin1" for "Hsin" and "lin2" for "Lin."
Either of these will get you a very close approximation of the sound, although the English meaning will likely be wrong since there is no way to know exactly which characters "Hsin-Lin" refers to without seeing them written out.