Liturgy (n): a rite or body of rites prescribed for public worship.
The liturgy of the Episcopal Church is found in the Book of Common Prayer. The "BCP" is hard to miss; its the red-covered book in the pew rack in front of you. The first BCP was written in the 16th century and has been revised several times since. The current version, adopted by the Episcopal Church in 1979, is in use by much of the Anglican Communion. The BCP helps to unite the Anglican Communion.
The center of Sunday services is the Eucharistic (Communion) Rite. The Rite has two major variations, Rite I and Rite II. Rite I uses more "traditional" language - for example, "It is very meet, right, and our bounden duty, that we should at all times, and in all places, give thanks unto thee, o Lord, holy Father, almighty, everlasting God". The more "modern" language of Rite II reads "It is right, and a good and joyful thing, always and everywhere to give thanks to you, Father Almighty, Creator of heaven and Earth".
At Advent, we use Rite I without music at the 8:00 AM Sunday service and Rite II with music at the 10:15 AM Sunday service.
The Holy Eucharistic Rite has two major parts - "The Word of God" and "The Holy Communion". In the Word of God there are three readings - one from the Old Testament, one from the New Testament, and a reading from one of the four Books of the Gospel. There is also a psalm which is said or sung in unison. These four parts are all prescribed by the Lectionary, an order of readings which operates on a three year cycle and is common throughout the Anglican Communion. The readings and psalm are chosen to have a common theme.
After these readings, the leader of the service (usually the rector) delivers a sermon which reflects upon the readings. The service follows with a recitation of the Nicene Creed (a prayer that, along with the Apostle's Creed, unites much of Christianity). The Prayers of the People follows, along with the general Confession. The Word of God closes with the passing of the peace and general announcements.
The Holy Communion begins with the Offertory, in which we offer our gifts.
The focus of the Holy Communion, is of course, the act of Communion. In the Episcopal Church it is our tradition to kneel when accepting bread and wine. At Church of the Advent, we feel that the table belongs to the Lord, not to us; all are welcome to share in the Communion. The act of Communion is preceded by the Eucharistic Prayer and the Lord's Prayer. A hymn is sung during communion. The service concludes with the post communion prayer, hymn, and dismissal.
A good introduction on what to expect at an Episcopal service can be found here.