Like any business, relationships are key.
I don't do a lot of sport photography, but it's probably about 1/4 of my annual sales. I have a loyal following who now come asking me to shoot for them, they volunteer to round up new clients for me, and they pull strings to get me special access to the field/court. All this started because a guy I work with knew I had started a photography business and asked if I'd be interested in taking some photographs of his son playing football...
The other thing is don't be afraid to rent some equipment, if you need it. Your fee may have to be adjust accordingly, but it'll be worth it. I can't afford to buy the 300 F2.8, but I can afford to rent it a couple times per year (get two shoots per rental period). The equipment allows me to get better shots, which increases my print sales. Definitely worth it.
And don't be afraid to charge - for your "session" and for your prints. If you're giving it away, you're only hurting yourself. Even as you're learning, your images will likely be WAY better than anything mom and dad can get from the stands with the P&S, so your clients will be happy. As you get better, they'll be even happier.
Carry yourself like a pro. It'll instill confidence in you and the client. Use contracts. Have a proof gallery with a limited number of images (only your best shots). Give them an order form. And deliver your images in premium packaging. That'll set you apart from the cheapies who shoot a jillion shots of anything and everything and sell the entire glut on CDs for $20 each. To me, that's not only horribly un-fun, it also doesn't lend itself to a professional appearance or a decent profit.
Just my two cents. To be taken for what it's worth, for sure, since I'm only a part-timer myself. If it weren't for my "day job," I'd starve to death...
Canon 7D Gripped; Canon 7D ii Gripped; Canon 17-55 f/2.8 IS USM; Canon 70-200 f/2.8 L; Canon TS-E 24 f/3.5 L; Sigma 85 f/1.4; Rokinon 8mm f/3.5; various lights & gizmos