After receiving the Holy Eucharist, it is customary for those who have participated to partake of the a piece of blessed bread ("the antidoron") and a sip of the wine mixed with warm water (the "zapfika") provided on the small tables ("tetrapods") on either side of the nave. While the bread that is distributed here is not consecrated, it is blessed, and as such, it should be consumed carefully and respectfully with care being taken not to drop the any crumbs. Because of the numbers of communicants, it is best that one simply take a piece of the antidoron and a sip of the zapifka (and please refrain from "dipping" the blessed bread into the wine). Parents and/or Godparents should take care to assist small children and to show the older children the proper "procedure".
Everyone that attends Divine Liturgy, Orthodox and non-Orthodox alike, may receive the blessed bread as an expression of love and the desire for fellowship in Christ. While we have the very nice custom at St John of the Ladder of giving guests and other non-communicants a portion of the blessed bread, if you see someone has already received this sign of hospitality please refrain from inundating them with several pieces. Finally, at the conclusion of the Divine Liturgy during the veneration of the Cross, all are invited to come forward to receive a piece of “blessed bread” as a sign of thanksgiving.
Let me know if you have any particular questions!