RR is spot on. Agents largely come from 3 groups - lawyers, former athletes and family/friends. The two latter groups basically have the same advantage of access to the athletes. Lawyers have the advantage of understanding contracts as well as things like collective bargaining agreements, salary caps and related labor issues and formal training in negotiation.
Because of salary caps in various sports, many of the highest profile athletes have simply been hiring lawyers and paying a fee to negotiate their contracts because the contracts are largely dictated by collective bargaining agreements. Instead of paying some agent a percentage of the contract (payable up front) to negotiate the deal, they just have a lawyer review the details.
One area where a business background might help is in sports & entertainment marketing. For someone looking to get into the business of sports, marketing would probably be the most likely bet so you should probably search out the best marketing schools.
The best way to break in to be a peon (likely unpaid) for a while before you are able to establish yourself in the business. It's like this in many parts of the entertainment industry and sports is no different.