What to Wear
Since the synagogue is considered a house of God, it is usually appropriate to wear nice clothes. On certain occasions that do not involve regular prayer services more casual attire is acceptable. Some synagogues are more informal, but usually women wear dresses and men suits. Younger children can usually get away with their play clothes.
Except in Reform temples, all men and boys (the little ones rarely keep them on) are expected to cover their heads. This is often optional at Refrom services. Out of respect even non-Jewish guests should follow the custom of the synagogue and wear a kippah. Men who have been Bar-Mitzvahed also typically put on a tallis. This is not expected of non-Jews, who may politely decline if offered one. Today, in more liberal synagogues women sometimes also wear a kippah and tallis, but this is not obligatory.
When to Arrive
Jews sometimes joke about operating on "Jewish Standard Time" in reference to their penchant for being late. Nevertheless, religious services usually start very close to a regular time, which varies among synagogues. Shabbat services typically start early Saturday morning and last for approximately 3-4 hours. People do not all arrive for the beginning of the services and it is not unusual for people to come and go throughout. Most services follow a regular schedule so it is possible to gauge when to arrive to avoid missing a particular prayer, the reading of the Torah or the rabbi's sermon.
The Prayer Books
The books used in the synagogue are considered holy (because they contain the name of God) and should be treated with respect. The reverence Jews have for their prayer books is reflected in the tradition of kissing one that has fallen on the g round. The regular Shabbat service uses two books, a siddur, which contains the prayers that are recited, and a chumash, which contains the Hebrew and English text of the Five Books of Moses.
The Torah Service
A selection from the chumash is read during the Torah service. The Torah is divided into "portions" assigned to every week of the year. Each portion is approximately three or four chapters long. Over the course of the year, the entire Torah will be read (in some Reform synagogues a triannual cycle is used whereby it takes three years to complete the reading). It is considered an honor to be called to the Torah for an aliyah (which means "to go up") to bless the Torah before and after chapters are read. The blessings are short and a copy in Hebrew with English transliteration is usually placed beside the Torah for people who haven't memorized the prayer.
When the reading is completed, the congregation stands while the Torah is lifted to show everyone the section that has just been read. A Haftorah is then read. This is a passage from one of the books of the prophets that relates to the Torah portion for that week. Depending on the synagogue, Bar/Bat Mitzvahs may read from the Torah and/or the Haftorah. Afterward the rabbi or the Bar/Bat Mitvah will offer a D'var Torah, a commentary on the weekly portion.
The Ups and Downs
A Shabbat service involves a lot of standing, sitting and bowing. Usually, whenever the Ark is opened to reveal the Torah, the congregation stands. At other times, there is no apparent reason for standing. During certain prayers, bowing toward the Ark is called for. Information on the specifics of these prayers will be added soon to the Library. Until learning the when and whys, it is possible to simply imitate those around you. If everyone else stands, so should you. The person leading the service will typically give instructions on when to stand and sit. It can be even more confusing when going to synagogues from different movements, which in a few instances stand and sit at opposite times.
Other Synagogue Activities
Synagogues are meeting places for the community and are used for a number of religious and non-religious functions. These include:
Sources: Judaism 101.