I have personal knowledge of someone (much loved by me) who transitioned. Process finally decided upon at age 28. It is a long, slow, complex path. If officially diagnosed as true gender dysphoria (a very small number of people) it is treated as any other illness.
Far too complex to go into the whole process, but it begins with drugs and surgery is almost the final process. It is not one simple operation either.
For a person to have truly transitioned, yes, 'privates' have been dealt with in one way or another.
I would add that it is a dangerous process and the drugs used have been known to cause fatal 'bleeds' on the brain.