Most here have explained what's most important for getting into the academy and the challenges the homeschooler goes through. But there are certain equalizers that you can concentrate on.
1. SAT/ACT: Take both and take them as many times as is available. Whether you are home schooled or not, the SAT/ACT is the #1 common denominator between home school, public school, private school, charter school, magnet school, etc... The SAT/ACT is probably the most influential portion of your application for academics.
2. Sports/Clubs/Organizations/Volunteering: The academy/military wants you involved in sports not only to ensure physical fitness, but also because of the "TEAMWORK" that is integral in sports. Same with the clubs, organizations, and volunteering. They want to ensure you are socially involved. The military revolves around teamwork and playing well with others. Most homeschoolers are still allowed to be on the local public school sports teams. This is your #1 choice. If not an option, then do community sports, city leagues, etc...
3. Leadership: In EVERYTHING you do, make sure you strive to excel in the activity and achieve leadership positions. There are certain leadership skill activities like Boy/Girl's state. But whether you are involved in scouts, CAP, sports, volunteering, part time work, etc... You need to strive for "Leadership" positions in the activities.
Best of luck. Mike...