“Never, never, never let anyone tell you that, in order to be Orthodox, you must be Eastern. The West was fully Orthodox for a thousand years, and her venerable liturgy is far older than any of her heresies.” –St. John Maximovitch (of San Francisco and Shanghai)
The Western Rite of the Orthodox church is a liturgical tradition within the Orthodox Church as a whole. Western Rite parishes are in full communion with the Eastern Rite of the Orthodox Church (are, in fact, a subset of the Eastern Orthodox Church). The primary differences are in worship style. Most Eastern Rite parishes celebrate the Divine Liturgy of Saint John Chrysostom, whereas Western Rite parishes typically celebrate one of the Divine Liturgies of either Saint Tikhon or of Saint Gregory.
Some of the fasting guidelines for the Western Rite differ from those of the Eastern Rite; this is primarily a result of how the Church of the West traditionally fasted. A good guideline can be found here; however, it is always advisable to consult with your Father Confessor regarding established fasting guidelines for your region.
The Antiochian Archdiocese and the Russian Church Outside of Russia (ROCOR) currently have active Western Rite parishes. Currently, all Western Rite parishes in the Antiochian Archdiocese (of which Christ the Saviour is one) are served by Eastern Rite bishops.
The Antiochian Archdiocese site on Western Rite Orthodoxy is a rich source of information, as well. Bishop Basil’s commentary is well worth reading.