How does All for One's "stealing quirk" work? Does he have to touch the victim, or can he do it from distance? Is this ever explained in the manga, official book, movie or something?
According to the Boku no Hero Academia Wiki, it is done through touch.
The process of giving and taking away Quirks is done through touch. People who have their Quirks stolen become Quirkless, losing any sort of abnormal features if they happen to be Mutant types. When quirks are stolen, the victim becomes disoriented and immobile for a short time. Meanwhile, Quirkless people who receive a Quirk through All For One become capable of manifesting all of its attributes.