If I go to an alternative medicine doctor, how do I know he is certified, what is their training like?

You don't know. As a medical doctor using a variety of innovative strategies to optimize health, I have no special license or certification that you can trust implicitly. I am regulated by the same medical board that other doctors are regulated. Good medicine comes in many forms. Being informed yourself is the best way to know if you are getting effective, efficient, and safe care - traditional or otherwise.
Possibilities. Certain branches of alternative medicine do have criteria for training as well as certifying organizations -- such as acupuncture, naturopathic medicine, massage therapy, etc. There are also extensive fellowships and board certifications for md's and do's practicing integrative/holistic medicine --http://www.Abihm.Org/ AZ, NV, and CT offer homeopathic/integrative medical licensure processes.