Is there anything special I'm supposed to do?

The general rule might be "sit when others sit, stand when others stand." During the silent standing prayer you may notice people bowing at certain points but don't feel that you have to imitate them. When you enter, you may see piles of prayer books (siddurim), either on a table, on a shelf, or sometimes in front of individual seats. Having one of these will help you follow the service and many have English on pages oppposite the corresponding Hebrew text (and the service itself will be entirely in Hebrew). It is hard for someone unfamiliar with the service to stay on the correct page, so, you may find yourself glancing at other people's books or having page numbers pointed out to you, or you may want to just not worry about it and take in whatever you can by listening and watching.

If it is a morning service, men will be wearing tallises (prayer shawls), and, on a weekday morning will be wearing tefillin (ohylactery boxes) on their arms and heads. You should not do either, though you should have your head covered with a hat, a borrowed yarmulke, or a yarmulke taken from a box that is sometimes to be found near the enterance (though not always).

Is there a special place where I'm supposed to sit?

Many men have their habitual places to sit (and when you go to the synagogue every morning and evening, the force of habit can be pretty strong, allowing one to essentially claim a spot). Sit where you like, but try to avoid places that are full of someone's personal things (e.g. books, cloth bags). Someone arriving later and finding you in "his" place may mention it or not. If so, you can look for another spot, or he may indicate that you should stay--levels of possessiveness about such things vary with the individual. You may want to look for a place near the back to be less self-conscious, but much will depend of course on whether there are ten other guys in the room or thirt-five.

I'm going with my wife where does she sit? She will sit in the women's section, where she will also possibly want to have a prayer book to follow along. The women's section may be on the same level or a balcony level. There will be some sort of divider or curtain which, in a M.O. shul will likely not be so much if an impediment to viewing the service, though the women do not participate in the public aspects of it. Unless the service is on Shabbat (Saturday morning) or a holiday, there are not likely to be many other women present, perhaps none at all, though there is no problem with your wife's attending even then. Jewish life is focused on the home, and women do not have the same obligation to pray communally at fixed times as do men.

Should I tell someone that I plan on going to the synagogue? It would be a good idea. Calling in advance and mentions whyans when you p,an to attend may make it possible for someone to anticipate what you will need a bit of help or guidance with to make the visit easier. Remember the Jews are not looking for converts, so there is no ulterior motive in receiving you. If anything, they will be more curious about your motive for attending.

What do I say if someone asks me questions? - What kind of questions will I get?