Many moons ago, when I worked as a manager in an eating disorders practice, we engaged in contract negotiations because parts of the typical ED treatments weren't necessarily covered by commercial policies. Because we were the only game in town that treated these conditions, and there was such a need for outpatient treatment, we had some leverage. If that's your situation, then you can set up your contracts to cover your typical treatment plans, with concessions for additional treatment based on clinical criteria. (think about how LCDs and NCDs are written). And I wasn't in the room during the negotiations. The data that was used to provide the rationale for our contract was provided by the clinicians, who had Ph.Ds, and lots of negotiating skills!
Otherwise, there isn't a one size fits all approach. It's very much contingent upon your specialty, the patient population, and what kind of contract they're willing to negotiate. However, a lot of contract negotiation (for the fee-for-service model) is done based on a percentage of Medicare. You may want to compare that figure with their fee schedule, to make sure that you're in the same ballpark, but if you're going to be sent patients based on your contract, then sometimes it's better to accept lower reimbursement if the bulk of the local patients are going to be funneled directly to you (think volume). If they need you for some particular reason, such as a sub specialty that they want to offer to their insured, then you can argue a higher percentage. Some contracts, such as risk adjusted contracts, are based on your performance with patient outcomes. If you don't have this data already analyzed, you'll be at a disadvantage, because frankly they have the data already-- and lots of analysts who can spin the information any way they want. So if you're better at treating patients than the guy down the street, you can use that to your advantage, as long as you negotiate a plan for those patients who don't fall into the bell curve.
Many physician groups take advantage of their PHO in order to enter into contracts that the hospital has negotiated on their behalf. To attempt to do this independently as a smaller practice up against a big payer is a brave move, unless as I mentioned above, you have a service that they want to be able to provide to their insured. I'm not aware of any coursework that could prepare you for this, but you would need to have some financial background, understanding of analytics, and negotiating skills.