What the Gospels say:
"At the foot of the cross of Jesus stood his mother" (John 19: 25).
"There was a garden at the place where he had been crucified, and in that garden a new tomb" (John 19:41 cf. Matthew 27: 59 and Luke 23: 33).
Therefore the Gospel affirms two things:
Signs of Mary's presence in today's Basilica of the Holy Sepulchre:
In the current basilica, people usually start by climbing very steep steps all the way up to the place of the crucifixion.
There, a mosaic reminds us that Mary stood up in faith, at the terrible hour of the crucifixion. It is also the place where Holy Mass in the Roman rite is celebrated.
A painting depicts Mary's suffering, the piercing of her soul announced by Simeon's prophecy: the sword represented on that painting is a symbol of her spiritual martyrdom.
Several icons represent Christ, Mary, and the beloved disciple, at the moment when Jesus gave his mother to John. It is the place where the Greek-Orthodox liturgy is celebrated.
When one goes down the stairs, one can venerate the stone where the body of Jesus was laid after his death. This is where Mary removed the long thorns from his head one by one and then washed the wounds of her tortured Son, with great love and compassion, but in haste since the Sabbath's rest was approaching.
Next, one enters inside the tomb itself, where the resurrection took place. Some walk around the tomb and reach a small Coptic chapel to touch and venerate the rock from the place of the resurrection. This little chapel is adorned with icons representing the Blessed Mother of God, her faith and ardent prayer as she waited for the resurrection. Christ is immortal because he is God, his resurrection means forgiveness, a new presence offered to us beyond the cross. This is why the prayer of Mary his mother was so important.
Finally, in the room where the Franciscans officiate, the chapel is dedicated to the apparition of Christ to his mother. This apparition isn't told in the Gospels—the sacred writers knew that such an apparition to the mother of the condemned one wasn't sufficient proof—but Pope John Paul II validated the long tradition of the Church that evokes such an occurrence. One of the arguments is that the risen one appeared not to crowds but to his disciples, to those who had followed him, and Mary is the first to have followed him.