Egeria was a nun who authored a detailed account of a pilgrimage to the Holy Land in the early 380s, making it the earliest of the kind. Regarding the Saturday of Holy Week, she writes:
Saturday of Holy Week
Now, on the next day, the Sabbath, everything that is customary is done at the third hour and also at the sixth; the service at the ninth hour, however, is not held on the Sabbath, but the Paschal vigils are prepared in the great church, the Martyrium.* The Paschal vigils are kept as with us, with this one addition, that the children when they have been baptized and clothed, and when they issue from the font, are led with the bishop first to the Anastasis.**
The bishop enters the rails of the Anastasis, and one hymn is said, then the bishop says a prayer for them, and then he goes with them to the greater church, where, according to custom, all the people are keeping watch. Everything is done there that is customary with us also, and after the oblation has been made, the dismissal takes place. After the dismissal of the vigil has been made in the greater church, they go at once with hymns to the Anastasis, where the passage from the Gospel about the Resurrection is read. Prayer is made, and the bishop again makes the oblation. But everything is done quickly on account of the people, that they should not be delayed any longer, and so the people are dismissed. The dismissal of the vigil takes place on that day at the same hour as with us.***
* The Martyrium is the main church in the Church of the Holy Sepulchre.
** The Anastasis is the Rotunda, or the Tomb of Christ in the Church of the Holy Sepulchre. Since the early days of Christianity, it was the tradition to hold baptisms on Holy Saturday.
*** Note that there are two liturgies done, one in the Metochion for the newly-baptized, and one at the Anastasis presumably for the faithful. The first liturgy would correspond to the Divine Liturgy done on Holy Saturday morning in the Orthodox Church today, which is really a Vesperal Liturgy. Interestingly, the second liturgy is done more quickly than normal, as it is also done today in the Orthodox Church. Also, absent from the account of Egeria is the ceremony of the Holy Light, or Holy Fire, which is not mentioned until the ninth century. Though she does describe a ceremony done daily at the Tenth Hour (4:00PM) for Vespers where lamps are lit throughout the Anastasis from a continuously burning lamb in the Tomb of Christ, and the light is so great from these lamps that she described them as an "infinite light." It is presumed that this Vespers ceremony evolved into the Holy Light ceremony for Holy Saturday.