The Quran clearly declared that Jesus (peace be upon him) as Son of Maryam several times. All the Muslims have the faith that Jesus (peace be upon him) was incredibly born with out any father by the Virgin Mary. Maryam in Arabic, the mother of Jesus is having a dignified status over the rest of women in the world and the greatest woman forever live.
Mary is having a dignified status over rest of the women in the world that how she happens to be pregnant with Jesus, with respect to Jesus, son of Mary, peace be upon him.
In chapter 19th of the Quran (that is called Maryam) the Mary receives an angle from God:
She separated from the family to a deserted place. She made a curtain from them and than then we (Allah) sent an angel to her (Gabriel or Jibrael), and he become visible before her in an appearance of a man like any human form. And the angle said that your Lord has chosen you for a righteous son gift. The Marry asked the angle that how I can conceive a son without a man, no man touched neither me, nor I am unchaste. The angle said it is very simple for our Lord and has already chosen you.
And The Miracle happens, Mary has becomes pregnant. Mary went out of the town to a deserted place in Bethlehem valley. It was 4 or 6 miles away from Jerusalem. She went with the fear that what will happen to her after the birth of the child. A voice came to console her, comforting and soothing her, and also guiding her. When Mary gave birth to a child, the voice guided her not to explain or speak anything and make a promise of silence, everything will workout.
After the birth Mary brings her child back to the village and meets elders and the Jews. They told her that she did a disgraceful crime. But Mary follows the instructions of her God (Lord). She was calm, quite and points to the baby.
The Muslims have total believe that the Jesus is like other human beings. He was born from a virgin mother, without the father and Allah created him like other human from dust. The Muslims also have faith that he is a Messenger of Allah; who does not lie and he is not himself is worshiped.
The Muslims also have faith that no Prophet has come between Jesus and Muhammad (PBUH). Allah has clearly declared his innocence in Quran.
As for as the Jesus killing and crucifixion, Muslims believe that as Quran says that they have not killed Jesus nor they crucified him but Allah made to resemble to him and Allah raised him to them. The Quran declared that Allah created you and you will be returned to him and Allah will make him return again.