Attend baseball games for fun and profit
Of course, not every ball will be worth a fortune. I doubt Steroid Alex Rodriguez was interested in paying for the ball from his 328th home run. But when and if he hits number 763 (breaking the record held by Steroid Barry Bonds)? He might well be willing to pay millions (in A-Rod currency, that's about a dollar) to obtain that ball for his trophy case. And even that lowly 328th homer ball will have value on the collectibles market.
More consistent pickings, however, come from the rookies. Any batter that plays in the major leagues (Duane Kuiper, career homer total of one, almost excepted) will eventually hit a homer, and that first home run ball can be worth quite a bit to them.
The WSJ interviewed one avid ball hawk about his strategy. He puts time into determining the most likely spot for a home run to leave the field and hangs out there. Variables to consider include which side of the plate the player swings from, the velocity of the opposing pitcher's pitches, weather conditions, and the end point of his previous homers.
My suggestion to someone interested in this business? Start with your local minor league club. Determine who the up and coming stars in the league are, and try to snag their homers. They'll be a lot easier to get, and eventually will be worth some dough. And even if you fail, you'll still have enjoyed some cheap entertainment.
One caution: ball hawking is a physical sport; the battle for a key home run ball can resemble a hockey fight.