It never really gave details in the song Remains of the day but the best guess is that she got bashed over the the head. The line 'and then baby, everything went black' is also a detail. And the mark on her forehead also is proof. What we know for certain is that she was murdered by her would-be fiance that she planned to elope with, Barkis, who (as implied by his behaviour and by what Bonejangles sings in Remains of the day) stole her family jewels and left her for dead.Contrary to popular belief she was not skinned. It is confirmed she looks the way she does from typical decomposition.
This answer contains spoilers: What happened was Emily found peace. She moved on. It was left vague so that the story could be accessable to all religions but the implication is that she is no longer in limbo but went to Heaven. The butterflies are symbolic of freedom. She learned to let go of her mortal ambitions. She allowed Victoria to have Victor. She did the right thing. And her murder got avenged. She found peace. There was a bright light and then she ascended in the form of butterflies.
The song Victor played on the piano (though many mistakenly think it was Moonlight Sonata) is actually an original composition by Danny Elfman for the film. It is called Victor's Piano solo and it's available on the soundtrack album.
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