How the story began came out in open letters (4,4,1,4)
I believe the answer is:
once upon a time
'how the story began' is the definition.
(first line of many fairy tales)
'came out in open letters' is the wordplay.
'letters' indicates an anagram.
'came'+'out'+'in'+'open'='cameoutinopen'
'cameoutinopen' with letters rearranged gives 'ONCE UPON A TIME'.
(Other definitions for once upon a time that I've seen before include "Fairytale beginning" , "Start of fairy tale" , "How to start of a children's story?" , "Tale opener?" , "Start of a fairytale" .)