The Jewish marriage ceremony has multiple parts, they are (according to orthodox tradition):

Kabbalat Panim

The bride and groom sit in different rooms. The bride sits on a "throne" that is usually on a small stage and receives her guests. The groom is surrounded by the male guests who sing and toast him.

Ketubah

Before the public ceremony, a private ceremony is held where the groom and two witnesses sign the ketubah (marriage contract), in most non-Orthodox communities the bride also signs the ketubah. The language used for ketubot is Aramaic and it outlines the groom's responsibilities to the bride.

Badeken

The groom is escorted by the male guests to the bride, all the while the men sing, and he lowers the veil over the bride's face.

Chupah

The public ceremony takes place under the chupah, a canopy that represents the home the couple will build together. Traditionally, the chupah was a tallit (prayer shawl) held over the bride and groom by four people. Today, a cloth canopy is used. The groom and bride are escorted to the chupah by both sets of parents. The bride then circles the groom 7 times, in which she is symbolically building the walls of the couple's new world together.

Kiddushin

The blessing for becoming engaged is said over a cup of wine, and the bride and groom drink from it.

Giving of the Ring

The groom gives an item of value (customarily a gold ring) to the bride; and, in Hebrew, declares his intention to marry her (see Tosafot commentary, to Talmud Ketubot 3a). He says to the bride: "Behold, you are betrothed unto me with this ring, according to the law of Moses and Israel." He then places the ring on her finger. Then a blessing is said (Talmud, Ketubot 7b). Technically, this actually constitutes the binding stage of the engagement, and in ancient times was usually done separately from the wedding ceremony.

Ketubah

At this point the ketubah (marriage contract) is read. The ketubah is signed by two witnesses and becomes the property of the bride.

Sheva Brachot

Seven blessings (see Talmud, Ketubot 8a) are sung over a cup of wine, and the bride and groom take a drink from the cup.

Breaking the Glass

This is probably the most famous part of a Jewish wedding ceremony. A glass or plate is placed on the floor and the groom steps on it to break it, to symbolize that even in this happy time, we remain aware of the Destruction of the Temple (Tosafot commentary, on Talmud Berakhot 31a).

Yichud

The bride and groom retire in privacy for several minutes to a room. This constitutes a symbolic consummation and finalizes the formal portion of the marriage. During this seclusion they break the fast which they observed on their wedding day.

Seudah

The festive meal. While the bride and groom are spending time alone together, the guests will move to the reception room/hall where the meal is held. At this time, the guests will line up on either side of the entrance to welcome the bride and groom with large amounts of fanfare. It's considered a mitzvah (good deed) to bring happiness and joy to the bride and groom so guests will dance, perform tricks, etc to make the couple laugh and entertain them (see Talmud, Ketubot 17a). After the meal, the Birkat Hamazon (Grace after meals) is said and then the Sheva Brachot are repeated.