It is really a "learn by doing" thing. I started as a committee chairman as a grade school kid in one of my clubs.
What volunteer activities are you doing? Get some and help plan some events. Learn to prioritize and delegate and follow up.
Really if you do this long enough people just associate you with being a leader. Examples below:
My professional society, I attended meetings for years without any involvement. Before long I'm asked to join the board, then I'm named president. So many people are afraid to be a leader that there is a vacuum created by apathy to be filled.
Chamber of commerce, after attending lunch meetings for a couple years, and taking part in two events, I'm elected committee chairman. Why? Everyone knows me and associates me with the group.
Running group. I'm not the fastest, but I had been with the group for 8 years and everyone knows me. Then the store hires me at their request to be the coach of the group.
A female friend is recounting how we met. I was attending the event the same as she was, but she recounts it saying I was the one putting it on and running it. I wasn't in the least.
If you are out front and meeting people and introducing them to your group, club, business, and taking a role, people look to you for leadership. Even if you are assisting people in putting something on, YOU are a leader in the participants eyes.