Ask a question that leaves room for a story
A few natural ways to open a conversation beyond the automatic job-title exchange, without turning small talk into an interview.

Start where you are
You meet someone new. Names are exchanged. Then comes the standard move.
"So, what do you do?"
There is nothing wrong with it. Sometimes work is interesting. Sometimes it is the obvious thing you have in common. But it can also produce the conversational equivalent of exchanging business cards.
"I work in finance."
"Ah, right."
And now both of you have to rescue it.
Try starting with something that gives the other person more than one sensible way to answer.
If you are at a wedding: "How do you know them?"
At a match: "Have you been coming here long?"
At somebody's house: "What have you been drinking? That looks good."
At an event: "What brought you along?"
None of these is a magic question. That is the point. They are just openings attached to the place you are already standing.
Follow the interesting bit
The useful move comes next.
Suppose you ask someone how they know the groom and they say: "We shared a flat in Manchester for three years."
You could jump straight to your own Manchester story. Or you could notice that they have just handed you several doors.
"Was that when you were students?"
"What was he like to live with?"
"Three years? There must be some stories you are allowed to tell."
The conversation starts to move because the second question came from the answer, not from a list in your head.
This sounds obvious, but a lot of conversation is two people waiting for enough silence to say the thing they were already planning to say.
Try the opposite for ten minutes. Listen for the detail that has some life in it and ask about that.
If somebody says they have just come back from Japan, "Where in Japan?" probably has more room than immediately telling them you once changed planes in Tokyo. If they say they spent Saturday rebuilding an old motorbike, ask what it is. If their answer about work suddenly becomes animated when they mention a side project, follow the side project.
You are not trying to extract a fascinating anecdote from them. You are simply letting their answer choose the next bit of the conversation.
Let it stay ordinary
There is a danger in advice like this. You can become the man at a barbecue trying to manufacture profound human connection while somebody is attempting to get another sausage.
Don't.
Small talk is useful. Weather, football, work, traffic, children, holidays and whether the pub has always been this expensive are all perfectly respectable things for two people to talk about.
And sometimes the person you have just met does not want to tell you a story. A short answer is an answer. Take the hint and move on.
The experiment is much smaller than that.
Next time you meet someone new, resist the urge to run through the usual questionnaire. Ask one question that has a little room in it. Then listen to the answer closely enough to notice where it might naturally go.
You may still end up talking about work.
It will just be because the conversation got there.