You need to follow the standards of care set out by WPATH. You will have to be living full time for a minimum of a year and on HRT for at least a year if there is no medical reason not to. You will need recommendation letters from a therapist or psychologist plus a medical doctor.
Most insurance companies and surgeons require a second therapist letter, not just one.
Finding a surgeon depends on whether you are MtF or FtM and what procedure(s) you have in mind. Options include individual practices as well as some university medical centers now (in the US, I don’t know elsewhere).
I want to say that when you research surgeons you’ll find that every surgeon has happy and sad patients. Going to a famous one (like Bowers or Meltzer for MtF) doesn’t guarantee no issues and going to Boston Medical Center (which started up a year ago and did a great job for me on a scar revision) is no guarantee of failure. Fame will guarantee longer waiting times though.
I do recommend being thorough and taking your time. Be 99.5% sure before going for it, you don’t really get a second chance if you’ve done the wrong thing. Surgical complications can generally be addressed.
One last thing. You have to go in with a reasonable set of expectations. For the MtF route that means keeping to a regular dilation schedule, and following the surgeon’s post op instructions carefully, most especially waiting long enough before any kind of sex. Expect dilation to be uncomfortable (still is after 30 months) but it’s just another chore.
Expect that healing fully will take a full year. It doesn’t mean you have to wait a year for sex but it does mean that things may not feel fantastic after just three months. It all takes a great deal of time.