General expectations for synagogue behavior include:
Dress: Guests at a bar/bat mitzvah celebration generally wear dressy clothes–for men, either a suit or slacks, tie and jacket, and for women, a dress or formal pantsuit. In more traditional communities, clothing tends to be dressier.
Arrival time: The time listed on the invitation is usually the official starting time for the weekly Shabbat service. Family and invited guests try to arrive at the beginning, even though the bar/bat mitzvah activities occur somewhat later in the service. However, both guests and regular congregants often arrive late, well after services have begun.
Wearing a prayer shawl: The tallit, or prayer shawl, is traditionally worn by Jewish men and, in liberal congregations, by Jewish women. Because the braided fringes at the four corners of the tallit remind its wearer to observe the commandments of Judaism, wearing a tallit is reserved for Jews. Although an usher may offer you a tallit at the door, you may decline it, if you are not Jewish or are simply uncomfortable wearing such a garment.
Wearing a head covering: A kippah, or head covering (called a yarmulke in Yiddish), is traditionally worn by males during the service and also by women in more liberal synagogues. Wearing a kippah is not a symbol of religious identification like the tallit, but is rather an act of respect to God and the sacredness of the worship space. Just as men and women may be asked to remove their hats in the church, or remove their shoes before entering a mosque, wearing a head covering is a non-denominational act of showing respect. In some synagogues, women may wear hats or a lace head covering.
Maintaining sanctity: All guests and participants are expected to respect the sanctity of the prayer service and Shabbat by setting your cell phone or beeper to vibrate or turning it off, not taking pictures, not smoking in the synagogue or on the grounds and not writing or recording tapes.
Sitting and standing: Jewish worship services can be very athletic, filled with frequent directions to stand for particular prayers and sit for others. Take your cue from the other worshipers or the rabbi’s instructions. Unlike kneeling in a Catholic worship service–which is a unique prayer posture filled with religious significance–standing and sitting in a Jewish service does not constitute any affirmation of religious belief; it is merely a sign of respect. There may also be instructions to bow at certain parts of the service, and because a bow or prostration is a religiously significant act, feel free to remain standing or sitting as you wish at that point.
Following the service: Try to follow the service in the siddur, or prayer book, and the Humash, or Torah book, both of which are usually printed in Hebrew and English. Guests and congregants are encouraged to hum along during congregational melodies and to participate in the service to the extent that they feel comfortable. During the Torah service, the entire congregation is encouraged to follow the reading of the weekly Torah portion in English or Hebrew.
The Bar/Bat Mitzvah Ideas and Primer for Interfaith Families is also available as a PDF document.