What is one thing I can do after school as a high school student to set myself up for a career in community management?

Volunteer, volunteer, volunteer. Build and scale your own online community for your personal passion. I started out this way building a community for women with disabilities, and then later worked on a community for artists, and a virtual world community - all as a volunteer.

Or, look around for internships at interesting companies. After some experience volunteering, I was able to intern at Disney Imagineering.

These two things directly contributed to me landing my first full-time job in this field.

Great question.  I always think there are actions we can take to prepare ourselves.  Think about some of the positions or job titles that perform community management functions.  You can contact those people or offices to inquire about job shadowing opportunities or internships.  This will allow you to see a day in the life of these people while performing their job duties.  Volunteering is also a good way to get to know many non-profit organizations in your local community.   

As the other answers mention, volunteering is a great opportunity to gain experience and hone these skills. Do you have volunteer opportunities through school? Could you start a community service project or a club at school? Find groups within the community that are looking for help with day to day activities and/or events. In school, I volunteered a lot with a group that helped children with back to school supplies, christmas presents, easter outfits and baskets, etc. I was able to help throughout the year with office tasks and preparing for these big events as well as leading up to and during the events.

Recently with AT&T, I did a community service project at a local charity that puts together lunches and snacks for kids during the summer that aren't getting that meal at school. I learned a lot about the organization, but even more so about the community they serve and their goals. This information is so valuable and will be a huge help if you're trying to get into community management. Lots of non-profits need day to day help. Try checking your local newspaper and magazines, school, library, or searching online in volunteer websites. I'm sure you will find someone that would love to mentor you and help you on your path to starting your career. Good luck!