I mean, how does a non-magic person find out that things like Hogwarts exist even if they do learn how to cast spells?
Okay, so how did Hermione find out about magic and is magic something that random muggles can be born with?
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Muggles can't do magic.
Muggle born witches/wizards (like Hermione) can do magic.
Muggle parents of magical children know about magic as a kind of "need to know" basis - they will be aware of magic because their child is involved (how does an 11 year old ask to go to a school they can't locate, need to go to a magical shopping place etc and do this in secret?) We know that muggle parents are aware of magic because Hermiones parent's took her to London to shop in Diagonal Alley and they went to Platofrm 9 3/4 at one point.
How does a non-magic person find out about magic - they don't. Or if they do (such as the campsite owner in GoF) memory charms are performed to keep magic secret.
How did Hermione find out - I'm sure it was mentioned somewhere that muggle borns get their Hogwarts Letter AND are visited to explain it to them.
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No they don't know magic. They probably found out about it after Hermione received her Hogwarts invitation letter, and she might have displayed signs of ability to do magic as a kid, which they might have witnessed. Muggles are generally not supposed to find out about magic in the muggle world. It's kept hushed up.
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I think they just know because hermione told them about it. They have to know because their her parents, or they would wonder where she is for months. They can't perform magic though.