The organizing principle of the Orthodox Church is “autocephaly,” which is a Greek word meaning, essentially, self-rule. St. Ignatius of Antioch wrote in the first century that where there are a bishop, a priest, and the people, there is the Church, and so the Orthodox believe.
The patriarchate of Jerusalem, the patriarchate of Antioch, the patriarchate of Rumania, the patriarchate of Bulgaria, the patriarchate of Russia, etc., are all self-sufficient. What they have in common is that they share the same faith and the same worship. There are of course linguistic differences, which have led to some musical differences, there are different local saints–though of course a common recognition of saints across the whole Orthodox Church–different iconographical traditions–though the basics are essentially the same–different architecture–as a Greek dome wouldn’t hold up under Russian snow, etc.
(Note that the “Assyrian Orthodox” aren’t actually Orthodox, but are Nestorians. The Patriarchate of Antioch–the city where the Acts of the Apostles tells us people were first called “Christian”–is the Orthodox patriarchate in Syria, Lebanon, etc.)
The way into the Orthodox Church is through the worship services. What town are you in? Is there an Orthodox Church in America parish in your town? If so, the services will be entirely in English. Go, and participate. If you read Sherrard’s book and want to know more, feel free to e-mail me at firstname.lastname@example.org.