I would second John's answer - learning more about statistics and statistical models will help you in your path of becoming a sports analyst. Many Stats professors at colleges have networks you can tap into that would hopefully help you find people in the field.
Many broadcasters working at both major and minor sports leagues have need for a data analyst or someone who gathers and analyzes data for them. Look for these kind of internships & opportunities as this can jumpstart your career in ways you can't imagine. Having a background in stats only makes you more competitive.
I think a lot of great suggestions have been made in the other answers shared. I would echo the advice given. Find a way to dive in data and stats. Today's sports are using more and more data and analytics to understand how athletes are performing and where they can improve. Taking a step to become knowledgeable in this field is a great first step and do so across all sports. As someone who is passionate about basketball I have been reading up on the use of analytics in the sport. Kirk Goldsberry has a great book out right now about how the NBA shifted to a prolific 3P shooting league. I suggest taking a look at Sprawlball! Additionally, listen to podcasts and find twitter accounts that are dedicated to data and stats.
Secondly, you can also begin finding a way to dissect film. It even may be as easy as watching games and paying attention to when analysts break down plays. Obviously, it takes having knowledge of the game to dissect film but you can learn a lot by watching and listening to others who are experts in the field!
Best of Luck,
Another career that may interest you is a Data Analyst (with a focus in sports.) These analysts provide the stats and analytics that go behind sports. They would be tasked with finding information such as: This player averages 30 points per game, takes 60% of their shots from this area, or this team has won 75% of their games at home. This type of career has less of a focus on communicating, but requires more technical knowledge.