Saucer separation

Saucer separation was an emergency procedure which could be performed by some types of Federation starships, and involves the complete disconnection of the primary and secondary hulls.

The procedure began to be incorporated into starship classes in the 23rd century, including the Constitution-class, but once the two hulls were disconnected they could only be re-attached through external support by a starbase or shipyard. (TOS episode: "The Apple"; comic: 'Til Death)

In the mid-24th century, Starfleet began to experiment with systems that were designed to allow the two sections to be able to reconnect without external support, and implemented it on several Excelsior-class vessels, including the USS Hood. As part of the training for use of the systems, all officers were required to train to perform manual docking should the need arise. (TNG novelization: Encounter at Farpoint)

The Galaxy-class was one of the first starship classes that were designed for separation with the two hulls having essential facilities which allowed them to operate independently for periods of time. However, with the Galaxy-class the system was designed to allow civilians and non-combatants to remain aboard the saucer section, while the main crew took the secondary hull with the main armaments to meet any threat that a starship could face. (TNG novelization: Encounter at Farpoint)

Examples of saucer separation
In 2267, the USS Enterprise (NCC-1701) was forced to separate the saucer from the engineering hull when an alien influence had forced the men and women to turn on one another, forcing Captain James T. Kirk to order the women to the saucer and the men to the engineering hull. Following the removal of the alien influence, both sections traveled to Starbase 13 for reconnection. (TOS comic: 'Til Death)

In 2364, Captain Jean-Luc Picard was forced to order an emergency saucer separation at warp speed following the USS Enterprise-D's first encounter with Q. While the saucer continued on to Deneb IV, the stardrive section confronted Q. The two sections were later reconnected in orbit of Deneb IV. (TNG novelization: Encounter at Farpoint)

A few months later, Geordi La Forge ordered a saucer separation so that he could return to the planet Minos and rescue Captain Picard and an away team, after the Enterprise had come under attack by the Echo Papa 607 weapons system. (TNG episode: "The Arsenal of Freedom")

In early 2367, the Enterprise separated as part of a tactical maneuver to confuse the Borg and allow a small team to infiltrate the vessel and recover Captain Picard who had been assimilated by them and turned into Locutus. (TNG episode: "The Best of Both Worlds")