Think in terms of layers. The most superficial questions are in the first layer: Where are you from? Where do you work? Where do you live?
First-layer questions aren't usually enough to help you find the leads to uncover a real likeness. It's the follow-up questions that allow you to penetrate the next layer. I've found that if you can "mine" a line of questioning down about six layers deep, you will surely strike gold.
If you ask someone where they're from, for example, and they say, "Little Rock, Arkansas, USA," you might think, "I have never been there, so we have nothing in common." You might then move on to another superficial question or end the conversation completely.
Or, you could reply, "Isn't former U.S. president Bill Clinton from Little Rock?" This might induce a response like, "Actually, he moved there after he became attorney general, but I recently saw him speak at the PMI® Global Congress." Ah ha! You've struck gold. Now you can ask more questions. "You were at the PMI congress? So was I. What did you think of former President Clinton as a speaker? Did you see any other presentations you liked?"
By eliciting the simple fact that this person had been at congress, you opened up many more possibilities for deeper questioning. Any of these could be a potential source of further questions.
Try it. With practice, you'll start to notice a spectacular phenomenon. You will become quite skilled at sensing where the "gold" lies. And you'll begin to discover you have affinities with practically everybody.