Seriously, right off the bat, you should recognize that you're going to judge a surgeon by different measures than you would judge a primary care physician by. For example, you're probably not going to have an ongoing relationship with this doctor, so you don't need to put much emphasis on his or her interpersonal cuddliness or bedside manner.
Most importantly, you want a surgeon who specializes in the precise surgery you need. Hunt for the specialist's specialist. You don't just want a doctor who is comfortable with performing a particular surgery as part of a wide repertoire; you want the surgeon who is obsessively focused on the specific technique that is the best choice for your specific surgery.
This is critical. For one example, cardiac surgeons used to do all chest surgeries, from attaching new vessels to removing cancerous lungs. Today, one surgeon can gain so much experience with one specific heart valve's repair that his or her patients have reproducibly fewer complications than the national average. For a second example, doctors who only perform nerve-sparing prostate surgeries have patients with lower rates of incontinence and sexual dysfunction.
Find out more about this book:YOU: The Smart Patient: An Insider's Handbook for Getting the Best Treatment