As a volunteer, there are a million ways to take initiative in the things you care about. While not every person needs or wants to take on a role in leadership, some may, so here are a few ideas:
There are so many clubs which focus on volunteerism for various causes — both in schools and adult life. Whether your school already offers them or you become a founding member, there are opportunities each year to become president, secretary, or social media manager. This club involvement is typically a low-stakes and high-guidance way to learn about leadership in community service settings. You may need to help promote service projects, seek them out, or do more universal things such as handle club finances and fill out forms.
Once you've put in the hours at a community garden or outreach group, you probably know what's what. If you want to take on extra responsibility, reach out to people and find out what's coming up. You can probably serve a role in keeping volunteers in line or helping with extra leadership tasks. Eventually, you might be offered a proper role, if you want it. By actively taking these steps, you're likely doing a lot for the cause you're involved in.
If you want to do something with a very tangible outcome, hosting a drive could be a great step. Finding an organization to partner with which takes donations, such as a food bank, dog shelter, women's shelter, or another group you're aware of, would be a great step. If you want to host a blood drive, contacting your local chapter of the Red Cross will open up the doors. You'll need to provide a location, volunteers for non-medical jobs, and donors, but the organization takes care of most everything else. If you have a passion for politics, providing information on voter registration, aka a voting drive, might be a good way to spend a few hours. In all likelihood, your local library or school has space to accommodate these drives. While some may depend on consistent volunteers, they can last for as long or as briefly as you want, and ultimately anything collected goes to a good cause.
If you have a lot of passion, time, and energy for filling a gap left by other organizations, you may want to start one! You can do so by identifying a problem, figuring out a way to address it, finding people to help you carry it out, and doing some sort of public outreach to make your organization known (such as on social media, promotional materials, or public announcements.) Once you do this, there may be people interested in financially supporting you. Before you get too far along in this process, registering in your state as a 501(c)(3) and gaining an employer identification number will likely be necessary. The importance of each step will vary based on the scale of your nonprofit. Ultimately, this initiative is something you will see the most impact with when you have the time and support to focus on it for years, so make sure you're treating it as the long-term investment it should be as you begin to explore your idea.
Leadership looks different for different people, so there's no wrong or right way to take on extra responsibility for a cause. If you genuinely care about something, you will probably lead well; when your heart is in it, your brain will catch up. Make sure that as you work on the cause you care about, you form relationships with people. These relationships don't just enrich your life, they make it so much easier to keep things running smoothly. You're learning alongside everyone else, meaning each individual has something to bring to the table. The world needs people who are willing to put energy into making it better, so go on and do it!