Last year, when I did my transfer. I had the approval notice with me. All I did was interview with the new company and when everything was negotiated, I told my old company that I was leaving. I sent my documents to the lawyer (same documents that you need when you are applying for the first time plus my approval notice).
I transferred in September. My OPT was valid till January but my H1B would start from OCT 1st. If any of this is not making any sense to you send me an email.