Verses 16-34 of Surah Maryam tell the story of Mary (SA) and Jesus (AS) from the beginning to the end. It is a magnificent story that comes in one page of the Quran but the points one can learn from it are numerous and can fill a book.
The summation of the story is that Mary (SA) was once in spiritual seclusion when God sent Jibreel (Gabriel) to her in the appearance of a handsome person.
Mary got scared, thinking he was a stranger who might have an ill intention. “She said: ‘Surely I fly for refuge from you to the Beneficent Allah, if you are one guarding (against evil). ‘I am the Messenger of your Lord, ' he replied, 'and have come to give you a pure boy.’ ‘How shall I bear a son, ' she answered, 'when I am not touched by a human and not unchaste?’ He said, ‘This is true but your Lord says, ‘It is very easy for Me. We have decided to give you a son as evidence (of Our existence) for human beings and a mercy from Us. This is a decree already ordained.’” (Verses 18-21)
So Mary conceived Jesus (AS) and went to a remote place in order not to face people. “When she started to experience (the pain of) of childbirth labor, by the trunk of a palm tree in sadness she said, ‘Would that I had died long before and passed into oblivion.’” (Verse 23)
“Then she heard the baby saying, ‘Do not be sad. Your Lord has caused a stream to run at your feet. If you shake the trunk of the palm tree, it will provide you with fresh ripe dates. Eat, drink, and rejoice. Should you see a person going by, tell him that on this day you have promised the Beneficent God to fast and never talk to any human being.’” (Verses 24-26)
When she returned to her people, some criticized her: “She took him to her people and they said, ‘Mary, this is indeed a strange thing. Aaron’s sister, your father was not a bad man nor was your mother unchaste’. So she pointed to him (Prophet Jesus). But they replied: ‘How can we speak with a baby in the cradle?’ He (the baby) said: ‘I am the worshiper of Allah. Allah has given me the Book and made me a Prophet. He made me to be blessed wherever I am, and He has charged me with prayer and charity for as long as I shall live.’” (Verses 27-31)
Then God assures that the story of Jesus (AS) is this and God, the Almighty, has never had a son and that His creation is such that when He decides to do something, He just orders it to exist and it comes into existence.