How can I improve people's leadership skills?

By teaching them the skills and put them through practical implementation of those skills. Assess the results and put them into more education and practce, if your see improvements. If they continue to fail they most probably can't make it because they don't have what it takes.

Through training 

Talk/Train/Discuss to the person and explain him what you need from him.Give time and freedom to take his decision and help him during the process in constructive manner.Have patience/faith in him.It is definately going to help him to improve as leader of future.

You should make them feel important, respected and valued, make them feel appreciated, ask for their opinions on various issues, respect their views, arrange for group discussions on various matters, and pay attention to each one of them, listen to them with interest, talk to them about goals, encourage them to stay focused, make the goals challenging, and make sure you reward and appreciate them suitably when they achieve these goals, make achieving goals a positive and enjoyable process. Remember always small things that can make all the difference such as  remembering their names, asking after their families, remembering their birthday dates or passing a compliment about their work, promote a happy, healthy atmosphere at the work place,  offer advice and praise as it is needed. By doing all this, you will be successful in leading your people by example and improving their leadership skills, because they will learn to do the same. Thanks