Although I am not direclty involved in performing face transplants, I have been following the procedure's progress over the last several years. Most recently, a group in Brigham and Woman's Hospital in Boston perfromed a full face transplant and the patient is now doing well and making good recovery.
People that receive face transplants are those that have full facial burns or trauma which have left them severely disfigured. They have to undergo a battery of medical and psychiatric tests to make sure they will be good candidates. The procedure itself involves a team of plastic surgeons who transplant the nerves, skin, and facial muscles of a donor onto the recipient. The surgery takes many hours and involves the use of careful microsurgery.
Unfortunately in this particular case, the patient also lost his eyes from his injury which are not able to be transplanted.
Read more in LA Times.