I was asked to give a little more information about the Byzantine Catholic church and what it is exactly. There's so much to tell about our religion, but I hope that you find this a little informative. If anyone is interested in learning more, please let me know. I will be more than happy to share my traditions with anyone!
What is an Eastern/Byzantine Church?
Byzantine Catholics are Catholics in union with the Bishop of Rome (the Pope) whom we recognize as the visible Head of the Catholic Church. We are recognized as being "Catholic" by the local Roman Catholic Bishops and the Bishops of the United States of America and the whole world.
(Byzantine Catholics are NOT Orthodox although they are practically "twins" in the religious world. One can attend a Byzantine service and then attend an Orthodox service and not tell the difference. Two main differences are the calendars of the church. Orthodox churches follow a different calendar. For example, today is Good Friday in the Orthodox religion. Also the Orthodox church does not formally recognize the Pope as the head of the Catholic Church.)
Having said that we are "Catholics", we must now state that we are NOT Roman Catholics, but Catholics who are identified as being Eastern Catholics. AS Catholics, we Eastern and Roman Catholics share the same faith and have the same seven sacraments. The difference is that we Eastern Catholics have a different way or rite of expressing our faith in regards to Liturgy and customs.
At the Last Supper, after Jesus changed bread and wine into His own Body and Blood, He told His disciples to "Do this in Memory of me." This they did. As the disciples brought the Gospel to different parts of the world, they adapted ceremonies of the Liturgy to the customs and music of that people. In the end, four great centers of Christianity emerged with distinctive Christian customs, but the same faith. These centers were located in the great cities of Jerusalem, Antioch, Rome and Alexandria. A couple of centuries later when the capital of the Roman empire was moved to the Eastern city of Byzantium and renamed Constastantinople, an adaptation of the Antioch way of celebrating Liturgy was made. Thus a new center of Christianity arose in Constantinople and her ritual became known as the Byzantine Rite. From Constantinople the Slavic peoples of Eastern Europe were converted by Sts. Cyril and Methodius and naturally followed the Byzantine Rite. Today the Byzantine Rite is subdivided into ecclesiastical jurisdictions based on ethnic groupings, such as Greek, Ukrainian, Ruthenian, Russian, etc.
The Christian Church was born in the Holy Land, what we call the Middle East today. As it spread, the Church took on the ways of the nations which accepted it. In this country, most Christian churches are 'western' because their roots are in western Europe, and their ways reflect the culture of the German, Irish or Italian immigrants who founded them.
Some American churches were started by people from Eastern Europe or the Middle East. They still keep the ways of the Holy Land (Jerusalem, where Christ founded His Church; Antioch, where the name Christian was first used; Damascus, where Saint Paul was converted) and their daughter Churches in Eastern Europe. Because our ways reflect this Eastern culture, we are called 'Eastern' Churches.
At the time of the early Church, there were several rich cultures in the Middle East and each of them has given rise to a different church tradition. The traditions of this church reflect the Greek or Byzantine culture, and so we are called Greek Catholics or Byzantine Catholics (from Byzantium, the ancient name for Constantinople).
Greek Catholics in the Middle East were also nicknamed 'Melkite' because they followed the faith of the Byzantine emperor, or melek. In addition, many Greek Catholic Churches are identified by their national origin, such as Hungarian, Romanian or Ukrainian.
In the United States, Byzantine priests and bishops are unmarried. In other areas, priests can become ordained as married men but cannot marry while priests; bishops are unmarried.
The Mysteries are visible signs of invisible graces, given to us by Christ. They constitute the nourishment of the Christian from birth to death.
Baptism - At Christ's command, the Church administers baptism to wash away sins, to purify, to protect against evil influences and to bring into the family of God as adopted children. Normally, baptism is performed on infants with the parents speakng the baptismal promises on behalf of their children. It is ideally performed by immersion.
Chrismation (confirmation) - This is performed immediately after baptism and infuses the recipient with the gifts of the Holy Spirit, to strengthen and enable the person to grow in the faith and, at maturity, to defend it. A special chrism (holy oil) is used to anoint various places of the body.
Eucharist - As Christ commanded at the Last Supper, we continue to receive Him into ourselves through the Eucharist. We receive immeasureable graces from this great Mystery and it is the mainstay of Christian life. In the Eastern Catholic Church, the bread, now become His Body, is mixed with the wine, now His Blood, and is administered into the mouth of the believer with a spoon.
Penance - As St. James reminds us, we confess our sins within the community of the Church. We confess to God in the presence of the priest, receiving the Church's assurance of forgiveness and spiritual guidance.
Marriage - This sacrament is often called "crowning", referring to the crowns used during the ceremony for the bride and groom. Christ spoke of marriage as indissoluable and in order to sanctify and strengthen the union of the man and woman, the Mystery of Marriage is solemnly performed. The marriage is consecrated with the Church as its witness and God as the provider of the graces needed for the new bride and groom to live, united in Him.
Anointing - St. James reminded us of the need to anoint the sick, and so the Church provides anointing to cleanse one bodily and spiritually. A special blessed oil is used to anoint various places on the body.
Holy orders - Those called by Christ to serve His people as spiritual guides and representatives of Him in the Mysteries are ordained with this sacrament. It confers a life-long seal on the priest and is a solemn laying on of hands performed by the bishop. The authority to perform this goes back in an unbroken line to the first Apostles.
THE LITURGY AND WORSHIP
The heart of Catholic worship is the consecration of bread and wine into the Body and Blood of Christ, as He instructed us. There are 3 Liturgies used - the one celebrated most of the year is the Liturgy of St. John Chrysostom, the Liturgy of St. Basil is said only a few times a year, and the Liturgy of the Presanctified Gifts is celebrated on Wednesdays and Fridays of Lent and the first three days of Holy Week. The latter has no consecration but uses the Precious Body consecrated at an earlier Liturgy.
The Liturgy of St. Basil is the oldest and was itself a version of the original Antiochene Liturgy of St. James, dating back to the earliest days. St. John Chrysostom further revised St. Basil's liturgy around the year 400 - today there are some additions and changes but essentially the liturgy is true to its heritage. The center of Eastern Christianity became located in Constantinople and thus the liturgy is also known as the Liturgy of Contstantinople and is that used by the Orthodox churches, the Eastern Catholics and some smaller independent churches.
Most of the Liturgy is chanted by both the priest and the faithful in English or Old Slavonic. The tradition of kneeling in the Roman church is not as widespread - standing is the ancient posture of prayer in the Eastern church.
The Sign of the Cross is made repeatedly during the Liturgy but in a different manner from the Roman Rite. We make the Sign of the Cross from right to left, holding our thumb and first 2 fingers together to symbolize the Trinity and with the last 2 fingers touching the palm, representing the two natures of Christ. Here is a link to more information about the Byzantine Cross (which looks very different than a traditional Roman cross) - http://www.byzantines.net/st-therese/cross.htm 
Rather than genuflecting, on entering and leaving church, venerating an icon or passing in front of the tabernacle, we make a reverence or mytania - bowing while making the sign of the Cross. Another custom is to approach the tetrapod on entering or leaving church and kissing the icon on it.
There are no musical instruments but instead a cantor who leads the faithful in intoning in unison the Liturgy. The chanting, called "Prostopinije", and the incense combine to remind us that we are in the presence of God, that this is the House of the Lord.
The Church year begins, not at Advent as in the Roman Church, but on September 1st, the Day of Indiction. There are other differences - some of the holy days occur at a different time - and the saints who are honored include the Eastern saints.
Sundays are usually named after the Gospel reading for the day or holy days which fall at that time. For instance, there is the Sunday of the Prodigal Son and the Sunday of the Man Born Blind.
In our worship special honor is continually given to the Virgin Mary. This is not simply a matter of pious devotion. In honoring her as Theotokos (Mother of God), the Church is affirming two basic aspects of Christian faith:
a) that the Jesus whom she bore is truly the Son of God incarnate, dwelling in our midst as true man; and
b) that the journey of theosis which was opened to us with her assent to Gabriel's message (Lk 1:26-38) has been realized in her person 'for this all ages to come shall call me blessed' (Lk 1:48).
Thus it is that we place the icon of the theotokos containing Christ in her womb on the eastern wall of our churches. This image, placed as it were between heaven and earth, recalls that it is through the Theotokos that God and mankind are Joined in Christ.