How to take good pictures of a group of strangers?

Almost all of us should know the moment, when a group of strangers asks you to take a picture of them.

I, of course, always agree but have yet to figure out a consistent way of getting people to smile for a picture and capture a genuine nice moment.

Don’t get me wrong, I always try to get a good shot and almost always do but I just wish to make those pictures more organic.

How do you guys do it?