Wow. Thanks for all the recommendations and advice. Having a church background that is non-liturgical makes it quite intimidating for us to visit on of the local Orthodox churches for the first time. I'm sure a copy of one of these books may help a little. Thanks again.
The good news is that it is never as bad as you think it is going to be.
Last year, on Good Friday, a friend and I attended a service (please forgive me I cannot remember the name of the service) at a Greek Orthodox parish in Florida. The parish was packed. We were clearly visitors and somewhat lost, but many people offered to help us understand what was happening and to translate some of the Greek for us.
The amusing thing is that I am 5'7", very fair skinned, with blue eyes and red hair. I'm of Irish and German descent and I look it. My good friend Karen is short (4'11") and much of her ancestry is Eastern European and Jewish. She has dark curly hair, a gorgeous olive complexion, luminous dark brown eyes ... and she's single. Everyone walked up to her and started speaking Greek immediately (especially the grandmothers and older ladies ... whom I suspect had a son, grandson or nephew they wanted her to meet). Sadly - no one said a word to me in Greek. Clearly I don't look Greek.
But everyone was warm, welcoming and very helpful.
If you are not accustomed to a structured liturgy then the first few times you go - don't worry about following along or knowing what is happening. Simply observe (stand and sit when others stand and sit) and let the Divine Liturgy wash over you. It will feel "foreign" at first. It will seem "odd" and you're likely to feel out of place. But I'd say that 99% (or more) of that is due solely to the newness of the experience and not because anyone else there thinks you're out of place.
Honestly? People who are there to worship God are not likely to be paying a lot of attention to what you are or are not doing. Unless of course you're doing something horribly disruptive and calling attention to yourself.
What I did at my first Eastern Catholic Divine Liturgy and my first Orthodox Divine Liturgy was to arrive early. Read through the Liturgy pew book before the Liturgy began to get a "feel" for the flow of things and then I put it in the pew and ignored it. I feared that I would miss too much if I spent my time flipping through pages hither and yon trying to figure out where I should be.
In short - go. Observe. Enjoy. The Divine Liturgy is awe inspiring - even if you aren't quite sure what is going on.