I have often been asked by new converts to Orthodoxy and even life-long members when it was appropriate for one to receive Holy Communion. This is usually the basic advice I give that I thought I would share with all.
Orthodox Christians are generally encouraged to receive Holy Communion at every Divine Liturgy. The purpose of the Divine Liturgy is to enter into communion with God, and the way this is done is by participating fully in the Divine Liturgy. One should avoid being late for the Divine Liturgy when receiving Holy Communion, as this shows a certain amount of disrespect for the great gift one is receiving, but if you are late you should not be later than the Gospel reading. The Divine Liturgy is the communal service and gathering of God's people (this is what the word "liturgy" means), so it requires full participation, as much as possible.
Many people worry and despair over the fact that certain sins in their life make them unworthy of receiving Holy Communion. However, as human beings who often sin every day, we are all unworthy of receiving Holy Communion and there is really nothing we can do to make ourselves worthy to receive the Body and Blood of Christ for the forgiveness of sins and eternal life. We should never approach Holy Communion saying "we are now worthy". But there are certain "grave" sins that we can commit that are sins not only out of habit (personal sins which require daily confession before God), but also sins against our fellow man that require resolve before receiving Holy Communion. For example, to bear a grudge against someone, to have hate towards a person, and to withhold forgiveness are all sins against our neighbor that require patching up before approaching the cup of love and forgiveness. As Jesus said: "Forgive and you will be forgiven" according to the measure that you forgive your neighbor. Some also have what are known as "sins against the Church" which require a general confession and repentance before a spiritual father or confessor (a priest) before one can approach Holy Communion, after a proper repentance to show one's humble approach before God's grace. Such sins are things like adultery, fornication, divorce, murder and heresy (holding blasphemous teachings opposed to the tradition of the Church).
Saying this, what is required for Holy Communion participation is summed up in the words said by the priest before distributing the holy gifts: "With the fear of God, faith and love, draw near". Humility is the most basic requirement, and trying to the best of our ability to live the life of the Church as set down by Christ, the Apostles and the Saints throughout history. The Church is a hospital for sinners, so the least we can do is to receive the "medicine of immortality" (this is what the Church Fathers called Holy Communion) acknowledging our sickness and seeking the entire treatment offered by the Church for our healing.