The Orthodox Divine Liturgy begins when the priest intones, “Blessed is the Kingdom of the Father, and the Son, and the Holy Spirit.” We need to arrive early enough to receive this blessing.   It is always appropriate to arrive in a timely manner, before the service begins. Doing so gives one time to get settled, to acclimate themselves to their surroundings, and to prepare oneself to offer themselves wholly in prayer. 
Arriving late without due cause is always inappropriate. Arriving late causes distraction and is inconsiderate to the rest of the faithful, to the celebrant and to God. The same can be said for leaving services early. Experience testifies that coming to Church late is more a matter of “habit” than circumstance: there are those who come late, and those who don't.
Some rules of thumb: Those who arrive late should generally refrain from partaking of the Eucharist that day as “proper preparation” for Holy Communion assumes the ascetical effort of arriving on time to the service and one should refrain from venerating icons or lighting candles in the front of the church so as to not distract others from prayer nor draw undue attention to oneself.