I assume that you are going to "pomen" or "parastos" which actually means "remembrance" and usually is held on the day when person died. Nikola Tesla died on January 7 which is actually orthodox Christmas.
There are no strict written rules of the etiquette, just a few general ones. Women are standing at the left side of the church and men on the right (watching from the entrance). I say standing because in orthodox churches there are no benches for sitting, at least not in Greece, Russia or Serbia, that I saw, maybe they change that in America by the influence of other churches. In the center of the church is usually long carpet (like a pathway) with some table (or box) with the icon of the saint patron of that particular temple. People usually enters in to the church walk that carpet to the icon, kiss the icon and put some change money in the box which is usually under the icon, and then go left or right. It is custom, not rule, you don’t have to do that, just go in and stand somewhere. You can enter and exit the church in any way you want, no rules, although some people are exiting the church with their back to the door and faces to the church, and crossing themselves like a mad. That is not a rule, just people playing "look, I’m religious".
Inside is different than catholic churches, there are no sculptures, and walls are usually covered with frescoes. The older the frescos are the more interesting they are (and they could go to the 11, 12 century in some monasteries). Newer frescoes (from 18-19 century) are a bit generic.
Maybe there will be some wedding or christening after the service, you can stay and watch that, like as any other event in the church. Churches are public places, so anyone can stay and watch.
Also there are no strict rules on dressing, it is just expecting from people to be dressed decently, so no flashy jewelry, minie skirts, fishnet stockings, crazy hats and such things. Pants or some long skirt is OK. You don’t have to cover your head with anything. People tend to do that but that is not a rule, I just asked my girlfriend’s friend who works in the church. Also she said that the idea is that all people are equal so that’s why they go modestly dressed in to the church.
The custom is to cross yourself (make cross sign with hand) as you enter and exit the church, you could do that in orthodox or catholic way or in any other way that you do in your religion. Also during the service people will do that several times, you could do that also if you wish, but you don’t have to, it’s not a rule, just custom.
When you enter the church you will see first the room with the candles (somewhere it is in small chapel made outside the church just for that). The custom is to lit the candle for the health of some person (if the person is alive) or for "peace of the soul" (if person is dead), candles for living person is up, usually at the chest height, and candles for the deceased are down, usually in some boxes at the feet height, sometimes it is just outside the church in some hole with the sand in it (in small village church i.e.). It’s OK too if you want to lit candle for someone you love (or loved, if deceased) even if you are of other religion, it is not forbidden, and in that way by buying the candles in the church you are making contribution to the church. In orthodox church usually there are no baskets for the money circling among people during service. You give money if you want with buying the candles, flowers, crosses, calendars and similar things.
If the service is held on sunday, and if church is in some smaller town, people usually stay sometime in the church yard and chatting, drinking or if the yard is bigger and weather is good, also some lunch or barbecue could be prepared (kids running and buzzing around, with stern looks from their mothers ;D). Although I doubt that is like that in America (big cities, people don’t know each other and that . . .)
Just be relaxed, Serbian Orthodox church is not so "serious" like roman catholic church, at least not in Serbia. It’s pretty cool and relaxed in basics, but unfortunately last 15-20 years everything becomes more and more to look like some bad grotesque play, even pathologic. Thanks to fall of communism and so called "awakening" of the religion spirit in Serbia, especially in bigger cities. I guess just like elsewhere in the world.
This all is how it is in Serbia, and what I know about all that, in America it could be different in some details, of course.
Here are two blogs about Serbs and Serbia (churches also) seen with the eyes of two American women:
_http://rosemarybaileybrown.blogspot.com/
_http://yankee-in-belgrade.blogspot.com/
Frescos from monastery Visoki Decani in Kosovo painted in 1350. The modern experts calls this "personification of Sun and Moon" :P
