The title of the best seller book from Dale Carnegie uses the word "win" in an odd way to me. The most common usage would be "How to Make Friends and Influence People", wouldn't it?
He's just using a different meaning win, where it refers to acquiring or gaining something as a result of a contest, like winning a prize. You might win a race in order to win a prize, but the prize is the only thing you take home with you.
In the context of Carnegie's book, making friends is treated as a challenge you take on for personal gain. The usage here is more like that in winning favour, or winning affection. Through the techniques the book teaches you, you will win people over as your friends.