Marty's presence in the past affected his mother's, father's, Biff's and Doc's only (also other people's lives but that isn't relevant). And thats the origin of their relationship. Doc gave Marty a part-time job to help with experiments, tend to the lab, tend to the dog, etc. Both of them were the black sheep in their respective environments.

when Doc found him there, he was delighted to find that Marty thought he was cool and accepted him for what he was. Marty snuck into Docs lab, and was fascinated by all the cool stuff that was there. So, being a red-blooded American teenage boy, age 13 or 14, he decided to find out just why this guy was so dangerous. But the history of the characters that Bob Zemeckis and I created is this For years, Marty was told that Doc Brown was dangerous, a crackpot, a lunatic.

As per a Mental Floss post by Back to the Future's co-creater Bob Gale: Okay, from the horses mouth (yes, Im the horse er, co-writer, co-creator): We never explained it in the movie. He pays me 50 bucks a week, gives me free beer.and gives me total access to his record collection - he's got this great old record collection. A couple of years ago he showed up at my house and hired me to sweep out this garage of his. In an early draft of the screenplay, Marty got to know Doc when he was 15 he would do odd jobs for him as an assistant, initially as an after-school job, but after some time they became friends: MARTY: Doc Brown's all right - he's just a little hung up on time.

Imdb back to the future 3