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Focus less on yourself and more on other people.
When you encourage your conversation partner to talk about themselves, Carnegie wrote, they wind up feeling more fondly toward you than they would if you'd dominated the interaction.
Nearly a century later, in an age where seemingly everyone has a digital platform for publicly broadcasting the contents of their breakfast, this idea is as relevant as ever - and people are still having trouble with it.
That's according to Dave Kerpen, founder and CEO of Likeable Local, a social media software company. Kerpen is also the author of "The Art of People," in which he offers tips and strategies for influencing people and forging positive relationships.
A common theme throughout the book is that, if you want to succeed in business and in life, you should focus less on yourself and more on other people. In other words: Be interested instead of interesting; listen actively instead of thinking about what you want to say next; and validate other people's thoughts and emotions after they've spoken.
"Listening is the single most important and underrated skill in business, in social media, and in life," Kerpen told Business Insider. "It's something we can always improve upon."
Of course, it's not as easy as it sounds.
"It's very hard," Kerpen said, "because when we have ideas that we want to communicate, our natural inclination is to talk about those ideas and to share those things."
But the less we talk, the easier it is to persuade other people to like those ideas and to like us.
Kerpen gave an example from his experience at Likeable Local. His chief technology officer, Hugh, is such a great listener that during meetings, "you sometimes don't even realize he's there because he's so quiet and he's always the last to talk."
When the team goes around the room and it's Hugh's turn to speak, he's usually silent for the first few seconds as he formulates an opinion. While everyone else was speaking, he was actively listening, instead of thinking about what he wanted to say in response.
"When he finally does speak, he'll be able to say something that synthesizes everything and makes his point in a powerful way," Kerpen said. "There's a competitive advantage to being the last to speak."
He offers another example in his book. Once, on a cross-country flight, he sat next to a lawyer and spent much of the flight asking the lawyer questions about his life, work, and family.
A year-and-a-half later, the lawyer became an investor in one of Kerpen's companies, thanks to the connection they made - due at least in part to the fact that Kerpen let him talk about himself.
"Remember that people care more about themselves than they care about you," Kerpen writes. "People want to talk about themselves. Listening and letting people talk is key to winning them over in life, in business, and in all human relationships."