A Synagogue (also known by the Yiddish word Shul) is a permanent Jewish place of worship.
The first thing I'll mention is that Jews can pray anywhere, and often do. Orthodox Jews will often pray the weekday prayers alone at home (although it's always best to pray with a Minyan). However, somewhere where prayers are held regularly should be consecrated as a Synagogue.
There is nothing intrinsicly holy about a Synagogue. The main room (sometimes referred to, especially in America, as the Sanctuary) can be large or small depending on the size of the Jewish community. The building will then often have other rooms attached to it, which can be used for teaching, study sessions, services for children etc.
All synagogues are different, but they all have some similarities.
- The Ark or Aron HaKodesh. This is the place where the Sefer Torah scrolls are stored. In Orthodox Synagogues, this is always on the wall towards Jerusalem.
- The Bimah. This is usually in the middle of the Synagogue, but can be at the front. It is where the Torah is read from, and often where prayers are lead from.
- Separate Seating. In Orthodox (and some Conservative / Masorti) Synagogues, Men and Women sit separately. In "Cathedral Style" Synagogues, the Women often sit in a high up gallery around the Synagogue. In more modern buildings, they sit around the men, behind the men, or sometimes the room is divided down the middle. If the men and women are on the same level, there will always be a separation between them. In most non-Orthodox synagogues, men and women sit together.
- Decoration. Judaism forbids the making of a graven image of G-D, and often this is extended to not even having pictures of people. However, there will often be stained glass windows around depicting the festivals or events from the Bible.
- Storage for members. Orthodox Jews won't carry anything in public on Shabbat (unless there's an eruv). So there is often provision for members to keep their Tallit at the Synagogue. This can take the form of a box under each seat, or perhaps a room with boxes on the walls.
Men should cover their heads when going into a Synagogue. Often you can take a Kippah from a supply by the door for people who don't have (or have lost) theirs. Married women should also cover their heads during a service.
Synagogues are usually funded by membership fees and donations. That said, a Synagogue will never turn you away if you can't afford to pay the fee, or if you're a visitor. But if you're a regular user of a Synagogue, it is only right to join up.
The Synagogue is usually managed by a board of management made up of elected members of the congregation. There are also a number of employees - most of them the obvious sort of people (a secretary, a caretaker, cleaners etc), and also in most cases the religious leaders - a Rabbi and perhaps a Chazan.