I think like with romance, there is a certain "click", a type of chemistry between two people that draws them together. Of course many times friendship does happen over time but many start with the connection.

For example although in theory I'd never advise it, I'm just becoming a friend with my client (it's just a short project anyway and almost done) because we had that click.

It's just a thing between two people that when they start talking they feel a type of mutual understanding and they have a great fun and interest in the conversation. Its easy and breaks the barriers of social pretense naturally.

You can find these people everywhere but it's rare and of course the real friendship also needs to survive the test of time and circumstances.