Transporters work by dissolving the sub-atomic bonds of the transport subject, converting the subject into an energy stream, then re-establishing the bonds in a new location according to a stored pattern of the subject. Living matter is transported at the "quantum" level, while everything else is transported at the "molecular" level. Quantum transport requires more energy and pattern storage. You may recall from the episode "Our Man Bashir," that when the transport of the runabout's crew malfunctioned & most of DS9's systems went down that the physical patterns were stored in holosuite memory, but it required the total storage capacity of the station to hold their quantum patterns.

Transport or "beaming" is accomplished as follows. Transporter "targeting scanners" calculate relative range and speed between target and destination, as well as verifying a suitable environment at the location. Transporter self-diagnostic routines are also performed at this stage. Next, the "molecular imaging scanners" create and store a resolution pattern of the subject (transporter trace). Each pad uses 4 scanners-3 of which must agree to permit beaming.

Actual beaming begins as the "annular confinement beam (ACB) forms a protective field around the subject. Within the ACB the "phase inducers" or "phase transition coils" accomplish the physical materialization/de-materialization of the subject. The matter stream is then routed to the "Pattern Buffer" for temporary storage. The buffer assembly includes special processors to adjust the pattern according to data previously gathered by the targeting scanners. The pattern is then sent to "emitters" on the hull, which transmit it to the destination. The emitter assemblies also contain long-range inducers & coils for beaming from a remote location such as a planetary surface. When beaming up, the pattern buffer is used to hold the subject for up to 7 minutes to permit biofilter & weapons scans or to allow for security or other personnel to meet the subject (subjects have no sense of time passage while in transport). The buffer also allows for site-to-site (internal) transport and as a safety in case of problems with the transport process.

Galaxy Class Starships have six personnel and four cargo transporters (cargo transporters can be adjusted from molecular to quantum resolution) with a range of 40,000 km. They also have six emergency evacuation transporters (beam out only) with a range of 15,000 km. Under emergency conditions a Galaxy Class Starship can evacuate 1850 persons per hour and beam up 1000 per hour.

(This material is summarized from the Star Trek: The Next Generation Technical Manual, section 9.0)