I don't think there's a formula. Usually, wherever I go, in time, I 'gel' or 'click' with somebody and then it is just so easy. Both of you have so much to say.
That has sometimes happened to me instantly and sometimes it takes time, so I still try to be myself even if I think people don't 'get' me....
Poshsinglemum, love the screen name, we have so much in common. Although I'm not competitive at all, which helps maybe. One of my best friends is a girl I've known since school. She wnet to country's best Uni, I went to an adequate one. She got a first, I got a desmond. Her first job paid her about twice as much as mine did, her husband is lovely, mine was a wanker, and yet we are STILL the best of friends because I take myself out of the competition where she is concerned. I'm confident that it is my personality she likes. She can't just replace me with a flourish of her wonderful-life-wand! If she wants my wit, warmth and humour {grin] she has to take me, mad x, single mother on benefits warts and all!
To pick up on another thing you've said, about making a new friend too much of your life too soon, I know what you mean. I think that's a good point. If you meet somebody you really get on with, take things calmly because they'll still be there next month probably.