It's not a huge stretch to assume that all muggleborns get a guide assigned who takes them on an outing to diagon alley. And they do have banks, obviously wizards have a way to exchange wizard money for human money so it has to work the other way around, too. Then again, it wouldn't have been hard to write that explicitly if that was indeed how it's supposed to work, and HP is the kind of world where they throw tons of insane shit at people and tell them to just deal with it.

And most likely, the author just didn't give it a single thought.