The last few decades have radically altered universally accepted ideas about the existence of social mores of dress and posture.
In every world culture and religion, certain outward practices are followed, in order to shape the inner life of individuals, and to unify people who share a common purpose or goal.
Saint Paul speaks about questions of dress and posture in the church (1 Corinthians 11, et. al). The entirety of Holy Tradition speaks to us on these matters as well. Even our holy icons show us the modesty of the saints, and the liturgical order of the Church - modesty and order we must emulate.
Volumes could be written on the history and rationale behind Orthodox practices, but some general rules can be helpful to all faithful people.
These are outlined below:
DRESS - Providing an example of modesty is important for faithful Orthodox men, women, and children. As a general rule, we should remember that we enter God's temple for all services dressed to meet the King of Glory. This means taking the time to wear clothing that is clean and modestly formal (i.e. neither ostentatious nor casual). Just as one would not wear shorts, beach wear, t-shirts, and other casual clothing to meet a dignitary, so too one would not dress this way in church. For those who cannot afford modest, formal dress for church, it is more than acceptable to do the best one can within one's means.
HEAD COVERINGS - Saint Paul and Holy Tradition speak to the question of head coverings in church: women wear them for the sake of modesty, men are specifically told not to wear them. Even bishops remove their episcopal miter during the Gospel and Eucharistic service. In this respect, both men and women are called to emulate the holy saints, particularly the Mother of God, and such practice respects the life and practice holy ones who have faithfully passed down the faith to us. By extension, one is called to modesty in all aspects of clothing in church (bare shoulders, muscle shirts, bare stomachs, high hemlines on skirts, etc.). Various means of head covering are used, depending upon the area (babushkas, bandanas, scarves, etc.)
POSTURE - The regular Orthodox posture for prayer is standing. If one is unable to stand for the entirety of the divine services, one should stand with reverence as much as physically possible, making a definite point to stand at the Entrances with the Gospel and with the chalice, as well as throughout Holy Communion (whether or not one goes to Communion). The faithful stand and bow when the priest or the bishop gives a blessing with his hand, the Gospel, the cross, or the dikiri and trikiri (bishop's candles).
PROSTRATIONS - Prostrations to the ground are made on various feast days and during services in Lent, and the faithful make a prostration during the Divine Liturgy at the consecration of the Holy Mysteries (when the priests says the words, "Amen, Amen, Amen."). Sitting during the sermon is always acceptable.