Many young employees are frustrated when their first jobs land them in powerless positions at the bottom of the organization chart after years of leadership roles in school, leading some to jump ship far sooner than employers would like.

How do you gain power when you have none?

More employers are opening new paths to leadership by encouraging employees to develop spheres of influence that have nothing to do with the org chart.

Such informal power is increasingly important—and valued—in today’s flatter organizations, where more jobs confer responsibility for teammates’ performance without the authority to give orders or dish out rewards or punishment, says corporate trainer Dana Brownlee, of Atlanta.

Specific behaviors can predict informal power, and many of them can be learned, she says. Networking across departments, building expertise in new areas and cultivating charisma are all ways to gain power, and make you a go-to person for colleagues.

People who build strong networks ask lots of questions of colleagues, show respect for co-workers’ roles and accomplishments, and look for openings to help with projects that excite them, according to a 2017 study of 20 employers and 160 managers co-written by Robert Cross, a professor of global leadership at Babson College in Massachusetts. “These people create enthusiasm in the networks around them,” making colleagues more likely to offer them new opportunities, says Dr. Cross, who heads a 70-employer consortium studying collaboration. “I call them energizers.”

Many people wrongly assume boasting about past accomplishments will make colleagues on a new job want to work with them. In fact, talking about your past record is “almost a death knell for credibility” because it fosters mistrust, suggesting you care more about promoting yourself than getting in sync with your new colleagues and their needs, the study says.

B.J. Shannon is “an extreme example” of the ability to build a strong internal network, says his former boss, David Niu.

Mr. Shannon, who headed customer relations for the past four years at Tinypulse, a Seattle employee-engagement company, forged warm, enthusiastic relationships with co-workers in all parts of the company, says Mr. Niu, Tinypulse’s founder and chief executive.

Mr. Shannon says he tries to “spread positivity” by showing genuine interest in others. He made a point of praising colleagues’ good work, sending at least five “cheers” a week on the company’s internal-messaging system, and tried to help others reach their goals, says Mr. Shannon, who recently moved up to a senior-management job at a larger company.

Prem Kumar, director of product at Tinypulse, says Mr. Shannon took a genuine interest in him from his first day on the job in 2016, and helped him learn new skills as he advanced from product manager to a more senior role.

Helping out your co-workers isn’t customarily seen as a path to power. But it can motivate others to embrace you as a role model—a valuable kind of informal power, based on social-science research, Ms. Brownlee says.

Increasingly, employers value this kind of influence, too. Employees with strong internal networks tend to be high performers, according to a 2016 study in the Harvard Business Review.

More companies are training employees to network, presenting it as a skill used by successful co-workers. Workday, a cloud-software company in Pleasanton, Calif., is piloting a one-day workshop where new hires learn how to build purposeful internal networks. Booz Allen Hamilton Holding Corp. , a McLean, Va.-based government contractor, encourages new hires to meet with colleagues recommended by their supervisors and explore ways to work together, says David Sylvester, director, global learning and development.

Limeade, a Bellevue, Wash., employee-engagement company, encourages employees to start “affinity groups” based on common interests such as golf or cycling, says chief executive Henry Albrecht. He believes employees who initiate such groups tend to be among those with the highest potential, he says.

Another route to informal power is to acquire needed expertise in an emerging area, such as helping others use the latest presentation software, Ms. Brownlee says.

Jay Bower, president of Crossbow Group, a Westport, Conn., marketing-services firm, advises new hires to actively seek out such opportunities. “Look for the thing nobody knows how to do or wants to do, jump in with both feet and do whatever it takes to solve the problem,” he says.

Soon after Mr. Bower took an entry-level job years ago as a marketing analyst at a retailing company, he got wind of a pressing, unmet need. The chief executive wanted an analysis of new data from an unexpectedly popular new customer-discount program. But the company lacked the staff to do it.

Mr. Bower asked the company’s head of information systems, Ron Gayda, to teach him a few of the analytical skills he’d need to do the analysis. Mr. Gayda, now a retired IT executive in Stamford, Conn., says he agreed because Mr. Bower seemed capable and hardworking, and he didn’t have enough staff in his department to do the work.

Working long hours to squeeze in the work among other duties, Mr. Bower finished the analysis, taking pains to give all the credit to his bos and Mr. Gayda, to avoid sparking resentment. The CEO was delighted, promoting Mr. Bower three times in his remaining 3½ years with the company.

Contrary to popular belief, charisma also is a quality that can be learned, says Ora Shtull, a New York City executive coach. “It means showing up as the best version of ourselves for the people around us,” and making a consistent effort to show authentic interest in others, she says.

Loan Mansy, a Philadelphia-based chemical engineer and client of Ms. Shtull, began her career as a production supervisor thinking she had to prove herself by asserting her views. “Everything was about me and what I thought,” she says. As she gained experience and worked with Ms. Shtull, Ms. Mansy learned it’s more important to focus on others, ask questions, listen closely and show warmth and empathy, she says.

She has since been promoted to a series of increasingly challenging jobs, to become an area president of a waste-management company.