Praise be to Allah.
Ruqyah is a vast subject and covers many topics such as Sihry (Magic) Masaha (Possession) and Ayn (Evil Eye). Ruqyah is the treatment relayed to us by the Prophet Muhammad (saw) for afflictions such as Sihr (Magic) Masaha (Possession) and Ayn (Evil Eye).).
Ruqyah is when a person recites part of the Qur’an such as Al-Fatihah or makes supplication using words transmitted from the authentic Hadith of the Prophet (saw) Ref. Fath-ul-Majid]
It was narrated that A’ishah (may Allah be pleased with her) said:
"When the Messenger of Allah (peace and blessings be upon him) was ill, he would recite al-Mu`awidhatayn (surahs of Al-Falaq and An-Nas) over himself and spit dryly. When his pain grew intense, I recited over him and wiped him with his own hand, seeking its blessing. " (Al-Bukharee).
What to recite to do Ruqyah for yourself or for someone else, there are many such du'as, most common are Al-Fatihah and Al-Mu`awidhatayn.
A group of the Companions of the Prophet (peace and blessings be upon him) set out on a journey and traveled until they came near one of the Arab tribes. They asked them for hospitality but they were refused. Then the leader of that tribe was stung, and his people tried everything to cure him but nothing helped. Then some of them said, "Why don’t you go to those people who are staying (nearby)? Maybe one of them has something." So they went to them and said, "O people, our leader has been stung and we have tried everything and nothing helped him. Do you have anything?" One of them said, "Yes, by Allah. I will perform Ruqyah for him, but by Allah we asked you for hospitality and you did not give us anything, so we will not perform Ruqyah for you unless you give us something in return." So they agreed on a flock of sheep, then he started to blow on him and recite Al-hamdu Lillahi Rabb il-`Alameen. Then he recovered quickly from his complaint and started walking, and he was completely cured. After that they took the flock of sheep, and some of the companions of the Prophet (peace and blessings be upon him) said, "Let us share it out." The one who had performed Ruqyah said, "Do not do anything until we come to the Prophet (peace and blessings be upon him) and tell him what happened, and we will wait and see what he tells us to do." So they came to the Messenger of Allah (peace and blessings be upon him) and told him what had happened. He said, "How did you know that it is a Ruqyah?" Then he said, "You did the right thing. Share them out, and give me a share." And the Messenger of Allah (peace and blessings be upon him) smiled. (Al-Bukharee and Muslim).
The du`aa’s that have been narrated in the Sunnah include the following: It was narrated that Ibn `Abbas (may Allah be pleased with him) said: "The Prophet (peace and blessings be upon him) used to seek refuge for al-Hasan and al-Husayn, and he would say, ‘Your father [ meaning Ibrahim peace be upon him] used to seek refuge with Allah for Isma`il and Ishaq with these words: A`udhu bi kalimat Allah al-tammah min kulli shaytanin wa hammah wa min kulli `aynin lammah (I seek refuge in the perfect words of Allah, from every devil and every poisonous reptile, and from every evil eye).’" (Al-Bukharee).
So let's always limit ourselves to the Shari Ruqyah, instead of Coptic exorcism.