We don't learn it. To pronounce new words, we do few different things.
We "sound out" new words based on the sounds we already know. If you know how to pronounce "time," you can sound out "lime." And for word parts that don't have a good sight-sound match, like the -ture sound in "picture /cher/," we memorize those word parts.
We learn how to use a pronunciation key in the dictionary. The idea is to match the spelling of a new word to the sound of a word you already know (an easy word).
symptom: y = the /i/ of him
syne: y = the /i/ of time
But we really don't memorize the phonetic alphabet. In fact, each dictionary can have its own variation of phonetic spellings, so memorizing one doesn't really help.
And we probably learn how to pronounce a huge number of words simply by asking someone who knows.
And because English spelling is so much fun, teachers like to give regular spelling quizzes and hold spelling contests. I used to love those, but for some reason I still ended up being a bad speller. : )