I too am shy and not a mixer. (As an example, I have been actively involved in my parish for over 34 years, primarily as an assistant chanter. We have a new presiding priest since a little over a year ago. I am amazed at how many people he inquiries about to me, and I know nothing more than to tell him how frequently they come to church; I don't know them.) Ask God to give you the mental presence to attend the Divine Services of the Church
Go in humility, which won't be difficult for a shy person; keep your head down, somewhat, try not to catch peoples eyes. Make an offering ($1.00) in whatever type of receptacle you see, take a candle, light it, and venerate the icon of the patron saint of the church. Be prepared to possibly encounter a "welcoming committee," Be polite, but not chatty. Take your seat, pick up a pew book which the church hopefully has, and follow the service. Hopefully you will enter a prayerful state. You may wish to remain in the church after the distribution of antithoron and await the priest exiting the Church after he has taken off his vestments. You may want to approach him about your possible journey into the faith. He may be rushed due to some need to meet with some group after church, but he should be able to suggest a possible meeting with you at another time, if that is what you want. Otherwise, you may wish to exit the church and return for the next week's service, until you are more comfortable in the church. Without intending to debate with my fellow Greek-American's, Greeks do not tend to be too friendly to those they do not know in a church setting, though that attitude is changing. That's a gross generalization and many GOAA parish's have adopted "welcoming committees," which hopefully won't be too invasive.
My response in this post assumes that you don't want to start mixing with people you do not know, because you are shy. You may "PM" me if you would like to discuss this further.