I am a doctor you must have heard about the case of a woman in UK who yesterday won the legal battle over her right to choose death. The judge decreed that the patients have the right to decide about whether they want to be treated or not, and if the patients wish to die the doctors have no right to persuade the patients to change their views. The patient is a woman who is on an artificial lung, that is, a ventilator. If the ventilator is removed she will die. The doctors say that these is less than 1percentage chance of her improvement. So the patient who has been declared mentally competent by two psychiatrists, has decided to die, and she has won the case. So my question is that as a practising Muslim, who is a doctor, what should one do when such a situation arises?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The mission of a Muslim doctor is to be a caller towards Allah through his actions and words. So, he should acquire enough Islamic knowledge to be able to perform this mission successfully. Thus, he can achieve two good tasks: treating hearts by guiding them towards Allah, The Knower of the unseen and treating the bodies as well.
It is not permissible for a doctor to help a patient for a sin. How would it be permissible to help in a major sin, i.e. to kill oneself? The Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever purposely throws himself from a mountain and kills himself, will be in the (Hell) Fire falling down into it and abiding therein perpetually forever, and whoever drinks poison and kills himself with it, he will be carrying his poison in his hand and drinking it in the (Hell) Fire wherein he will abide eternally forever; and whoever kills himself with an iron weapon, will be carrying that weapon in his hand and stabbing his abdomen with it in the (Hell) Fire wherein he will abide eternally forever" [Reported by Imams al-Bukhari and Muslim ].
It is strictly forbidden for a doctor to remove something from the body of a patient, which can harm him/her or cause him/her death.
You should explain to the patients the dangers. If they are not convinced by your advice and you can prevent them from doing a harmful act you should do that; otherwise, at least you should not be involved in that act. Allah burdens not a person beyond his scope.
Allah knows best.