Okay, here is the quick and dirty scoop on Orthodoxy.
The Orthodox Church traces its roots back to the day of Pentecost when the Holy Spirit descended on the Apostles in the Upper Room. It considers the twelve Apostles to be the founders of the Church, and that Christ is the head of the Church.
Up until 1054 A.D. there was only one Church. It was simply known as the Christian faith, and did not have a denominational name attached to it. Then on a warm afternoon in 1054, during Divine Liturgy (Orthodox term for service where the Eucharist is consecrated and served) in the Cathedral of Holy Wisdom in Constantinople, representatives from Rome came in, and in a not-so-nice manner
formally announced that the West was splitting from the East.
After the split, the Western Church was known as the Roman Catholic Church, and the Eastern Church became known as the Eastern Orthodox Church. (Not to be confused with the Oriental Orthodox or Coptic Orthodox Churches.)
Eastern Orthodoxy worships in a liturgical fashion. We use the Liturgy of
St. John Chrysostom, which was written about 1500 years ago. Like the Roman Catholic Church we have Bishops, Priests, Deacons, Sub-deacons, Readers, etc. With the exception of the Bishops who must be celibate, all of our clergy can marry. (Bishops can be widowed.) Also, unlike the Roman Catholic Church, we do not have one Supreme Bishop. It is a conciliar church where all of the Bishops are first amongst equals.
The beliefs of the Orthodox Church are based upon the Holy Traditions handed down to us by the twelve Apostles, the writings of the Holy Scriptures (the Bible), the receiving of the Holy Mysteries (baptism, chrismation, communion, marriage, priesthood, and holy unction/healing), the teachings and writings of the Holy Fathers (and Mothers), and the Divine Liturgy.
In regards to your question about the Greek Orthodox Church, Orthodoxy has always been preached in the vernacular, and has always flavored itself to the different customs and traditions of the land that it was being preached in. So when the immigrants of Eastern Europe came over to the United States, they brought with them the traditions, customs, and the faith of their homeland. Thus, you will see different Orthodox Churches with different nationalities before the word Orthodox in the Church name. This is how we have Russian, Greek, Serbian, Bulgarian, Ukrainian, etc. Orthodox Churches in the United States. (Years ago this was also common in Catholic Churches; Polish Catholic, Italian Catholic, Irish Catholic, etc.) As years have passed, the Churches have become less ethnic (some still remaining more ethnic than others) and we are working towards a true North American Orthodox Church. (But thats a whoooole other discussion in and of itself!

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Here are some great websites that will teach you more about Orthodoxy:
Greek Orthodox Archdiocese of America
Orthodox Church in America
The Self-Ruled Antiochian Christian Orthodox Church in America
OrthodoxWiki (Orthodox version of Wikipedia)
Hope this helps!
In XC,
Maureen