The best way is to get a degree at a large school with a strong sports management program. The reason i say a large school is because the best way to get your foot in the door of a major sports team is to connect with an alumni of your school who has a high ranking role for said team. Some examples of schools with big programs and successful alumni are UMass Amherst and Boston University. Not only are these colleges located in the best sports city in the country also known as the city of champions, but they also have current MLB and NBA GM's that graduated from there programs. These GM's are often more likely to take interviews from students from there university. Also, they both have elite programs that if you do well will help you get your foot in the door regardless of alumni assistance.
I would look into applying to Umass it's also very affordable.