How to pet a cat n whch are the most friendly cat,?

Ask the owner if they think it's ok, first of all, since they'll know if it's bad with new people etc, if they say it's ok then you just need to make sure the cat's familiar with you before you try to stroke it. It's a pretty human requirement, I'd need to be at least on first name terms before someone rubs my back ;).

Moving smoothly hold your hand out near them and let them smell it, if they recoil you've scared them and that's when they'll scratch to defend themselves. If it seems calm just, continuing to move smoothly, run your hand in straight lines along the ridge of its back running from head to tail. If it gets bored it'll start swishing its tail (it's the opposite from dogs - happy dogs wag while cats swish when they're not) and you should just leave it alone. Don't push down on its back, just rest your hand and move it along in the same direction. Few cats like it if you go against the grain of their fur.

Once it's more familiar with you you'll learn the give and take involved in stroking a cat's head etc but if you're only meeting it for the time familiarising yourself then you just need to stroke its back (or not if it doesn't like you, just let it relax and try again after 10 mins or so but don't pressure it).