We have a freelancer that we work with that does this.
Here's a little advice.
First, don't expect to sell a lot. Unless you're advertising like crazy, you're likely going to shoot 500 pictures for every one photo you sell.
Second, be sure to know what the local copyright rules are for the league(s) you plan on shooting. Some state associations, for example, sell their photos through a company and may have an exclusivity deal that prevents you from doing the same.
I've found that if this is the case, chances are you're only going to bump heads with the higher ups at championship/playoff games.
Third, make sure your web site has an easy to remember name and is well organized/easy to navigate. For a lot of people, they're only going to your site to see if you have pics of their loved ones and seeing the photo is often enough to satisfy their curiosity.
Fourth, make sure you know your audience. Some schools are going to have more affluent parents who are more likely to have money to spend. That doesn't mean stereotype though. Just because you think a poor, inner city school has a cheap fan base doesn't mean it's true. Know your market and keep track of who buys things from you.
Fifth, be prepared to do a lot of traveling. If you limit yourself to 1-2 schools in your area, you're really killing yourself in terms of branching out and making the most out of your time.
Sixth, be prepared to go to sports you might not like. (Cross Country and Track are great ways to get a ton of photos because you can stand in one spot and just shoot each person one at a time.)
Seventh, be prepared to go the extra mile. A lot of freelancers just take photos and put them online. If you want to distance yourself from the competition, ID everyone. Make the name searchable.
Eighth, find out about how this will affect your freelance fee. Depending on what newspaper you're at, you might be able to shoot a game for them AND for yourself at the same time. The guy we work with sells all the photos he shoots and we have a deal where we pay him a flat rate every week to run pictures.
Lastly, get to know your community. Just having a business that caters to local sports doesn't mean it will be a success. Talk to fans/parents. See if there's anyone in particular they want you to get pics of.
Oh, and one more thing: have fun. You're not likely to become a millionaire off of this thing. But, if you're always having fun shooting and whatnot, it will never feel like work and that makes the money even more enjoyable.
Good luck.