I'm sorry to tell you that you've picked the worst possible time to get into sportswriting. It's awful out there. Really awful. There are more talented journalists laid off each year than there are new jobs, and that's even before you start adding a few thousand eager college grads to the market.
I think that's the most important thing to know: That the odds are stacked against you.
That said, it can be done! You have to be, to borrow from Scrooge McDuck, "Smarter than the Smarties and Tougher than the Toughies."
A few years ago, even, it was possible to break into the business for almost anyone, as long as you were willing to start low enough. I got my start at a paper with a circulation of less than 5,000, in a town so remote that the publisher almost tried to talk me out of taking the job out of hiring me, because she was just trying so hard to make sure I understood how far away from civilization I'd be so that I wouldn't arrive and then quit. I was the only one to apply for the job.
Now, even those jobs get 50 applicants the first day they post a job opening. But that's very likely where you'll be starting. Is your love of sports journalism that great? Are you willing to move halfway across the country to some forsaken farm town to cover basketball games between two schools with a combined enrollment under 100?
Great! Here's a little good news to end it on: While the bottom of the job barrel is no longer so easy to scrape, the top of it is no longer quite the long haul it used to be. Getting to the big time used to be like working your way up through the minor leagues in baseball: a long, slow process. You stopped at progressively larger papers every 3-5 years, and after four or five such stops, you were working at a major metro.
These days, on the very rare occasion that a major metro is hiring, they don't care that much about experience. They mostly just want someone young and cheap. If you are truly more talented and a better interview than a few hundred other applicants, then having just a few years experience is enough to get a major pro or college beat!