How can managers develop leadership skills?

By listening to subordinates and by having a greater vision and making his team strong and like a family.

Firstly, placement of managers are because they have leadership skills however, since leadership skills is a generic and covers various areas of business , I would say some skills have been obtained prior becoming a manager. In relation to this question, as leaders always learn as I believe leaders are made not born , I would the following: 1) self reflection and analysis of the skills you have obtained by keeping in mind your actions and reactions of your external environment. 2) seeking help from human resources manager to analyse the weakness or lack of skills needed to improve. 3) Engaging in informal talks with peers to see what is lacking in the system while leading.

Successful and effective leaders get to be that way by responding positively and adaptively over a long period of time to diverse but specific experiences. Basically, these can be grouped into the below types :

Challenging jobs. Challenging jobs—starting up something or fixing troubled operations, expanding large operations, working on time-limited projects from crises to systems installation—

Hardships. Hardships teach executives about their limits. These include making mistakes, getting stuck in dead-end jobs, enduring the traumas of life such as untimely deaths and tornadoes, and having to fire people.

Off-the-job experiences. Experiences off the job, usually relating to community service, can be primers in persuasion. Each of these types of experience teaches something unique, and learning from a variety of experiences can lead to one's being a manager with balance, able to respond adaptively to a variety of challenges.

Start-ups. Start-ups are assignments in which the manager starts from scratch to produce something—for instance, products, plants, or subsidiaries.

Fix-its. Fix-it jobs—for instance, turning around troubled units or integrating feuding or nonaligned departments—teach managers about both building and using structure and management and control systems, as well as how to cajole and persuade others that the new ways and systems are better than the old.

Line-to-staff switches. Moving from a finite, measurable line job to a corporate staff planning job is one of the most focused ways that managers learn to think strategically. Line managers who think they understand planning often see it quite differently after they have moved into a staff financial or business planning assignment and looked at the practices in other units, analyzed various financial scenarios, or scanned what competitors have done.

Savvy managers focus on developing skills in those employees with natural leadership abilities as well as those with a desire to learn leadership through training and work experience

They can develop their leadership skills through cultivate the spirit of team work,get the work done and problem solve skills.

let the other team mates take the initiatives and stand by with them, if they take initatives they will learn something new. providing feedback. welcome their ideas, 

By acknowledges the needs and concerns of others, promotes a positive working environment, has loyal and committed workers, manages different personalities and be tactful and sincere among others.

By learning from their misstakes and to be available for their staff and adherant. 

Make a practies and training 

usually it is inbuilt and natural but yes one can develop some skills by reading, training, following inspiring personalities in your life at work or home or society, practicing the same at work and in personal life.  

if you are a manager, it becomes a responsibility to be a good leader or else you are preparing to fail

The world we want to experience is where everyone leads with integrity and embraces living in possibility. Where anything is possible. Where everyone sees their own gifts and finds ways to use them for the greater good. We want to see our best selves.