First, you fill out an insane amount of paperwork, supplying the hospital with your kindergarten report card and every piece of degree paper you've gotten since then. On second thought, be prepared to document your APGAR scores. Then you answer 200 questions of the form "Do you sell illicit drugs?", then you document recent CME, your high school band attendance record and every other form of education you've had. Then you provide them with a bunch of references from your fellowship. Then you sign another 100 forms. Then you submit and get told you didn't provide proof of your infant vaccinations.
Some documentation of completing residency and fellowship is needed as well as evidence of state licensing (or at least in progress ) to start the credentialing. Also, as a pedi cards doc if you are asking for procedural credentialing, you'll be asked in some form to document your training in that procedure and then the head of the group (e.g. division head of pedi cards) will be asked to review it and accept it as evidence of adequate training and experience.
Any meaningful overseas training would need documentation and if not in English, certified translation. I also forgot to mention that they will ask about malpractice lawsuits or other legal actions you may have been involved in.