There is a prayer service in the Orthodox practice, which is called "prayer before surgery". In the text of the petitions the priest says that the Lord has arranged the mind and hands of a surgeon for a safe transaction. Often Christian believers before surgical surgery turn to God through this prayer.
Also before surgery, you can pray the most Holy Theotokos before her icon called "Healer" to the virgin Mary you Can also order the prayer in the Cathedral or find a prayer book that contains the prayers before this miracle-working image of divine Mother.
In the Christian tradition there is a practice of appealing to the saints with a special grace to help sick people. Thus, believers pray to the great Martyr and healer St. Panteleimon, who even during his lifetime he healed many patients. Holy you can request a special prayer service in the Church and to put candles about health of the sick.
You can pray to your guardian angel and Archangel Rafail responsible for people's health.
In the Orthodox Church is the Holy, which before the taking of Holy orders was very famous Russian surgeon. It was St. Luke Voyno-Yasenetsky. Great man of God graduated from the days of his earthly life as a Hierarch of the Orthodox Church. This Holy pray for the assistance in disease and, of course, before surgery.