Here is the Washing of the Feet at the Patriarchal Cathedral of the Resurrection in Kyiv served by Patriarch Svyatoslav earlier today.
The Washing of the Feet in the Byzantine Churches is performed only at Hierarchal Liturgies, be it at a cathedral with the bishop or a monastery with the abbot. For reasons that are pretty obvious on the face of it, you must be a priest to get your foot washed, since the 12 Apostles were priests. After the Ambon Prayer at the end of Divine Liturgy, the deacon chants the Gospel of the Washing of the Feet and the bishop and 12 priests perform the actions as the deacon chants them. The verse stating that Christ washed the feet of the apostles is repeated 12 times. The final priest fulfills the role of St. Peter. The bishop chants the words of Christ and that priest chants the words of Peter. Since they are both ordained, there is nothing wrong with them saying lines of the Gospel reading. Then the bishop re-vests and says the blessing and dismissal as usual. In parish practice, Vespers of the Mystical Supper and Divine Liturgy of St. Basil on Holy Thursday evening simply proceed without the Foot-Washing.