What should I wear to an Orthodox church and how should I act?

Think wedding casual. If you're a man, slacks and some kind of polo shirt at minimum. If you're a woman, a knee-length skirt or dress, something modest that covers you up, and a head covering, which was the norm in all of Christianity until about 100 years ago. If you wouldn't wear it to somebody's wedding or a formal event, you shouldn't wear it to church.

Shorts, t-shirts, running shoes: that is not the dress code for the most incredible miraculous event in the entire universe. As far as etiquette, just stand. If you see people making the sign of the cross, you can make the sign of the cross. If people bow to the priest for a blessing, you can bow. It's monkey see, monkey do, and you're not expected to do anything.

If you're a visitor, nobody is going to be offended by you being there. They all know you're new, they were all new once, and nobody is judging you or paying attention to you. If they are, they're paying attention to the wrong thing, because they should be paying attention to Christ.