Teleportation is a form of matter transmission and can be one of either a process of physical/psychological will or a technological interaction.
Mental teleportation
The Kitlings and those affected by the Cheetah World could teleport away from their home to hunt for prey, and then return through what was a physical (or possibly psychological/instinctual) process. The ability could also be transfered as Ace, Midge, the Master and the Doctor all acquired the ability, although it was not permanent in the majority of those who were affected. (DW: Survival)
The Eight Legs of Metebelis III could also teleport, both themselves and the Humans that they hung onto, most likely through the psychic link that was developed between the Eight Legs and the Human. (DW: Planet of the Spiders)
Technological teleportation
In the case of a technological process, Clockwork Droids possessed a short range teleporter (DW: The Girl in the Fireplace) and the Lady Cassandra O'Brien possessed a long range teleporter, although her use of teleportation was forbidden under Peace Treaty 5.4/Cub/16. (DW: The End of the World)
Also, in the case of teleportation through technology, a signal is needed for the teleport to work. The signal needs to be broadcast close to the person or item being teleported. The signal can also be reworked to teleport a person back after they had teleported away. (DW:The End of the World, Boom Town).
The planet Sto (or at least Max Capricorn Cruiseliners) also has a form of teleportation, the full range of which is unknown, however it’s range is at least enough to teleport from a ship in orbit to the Earth’s surface. It uses bracelets, which can detect whether any mishap has befallen the wearer, and can signal the system to hold the molecules of the wearer in stasis as a safety feature. The wearer can then be brought back to the ship, provided that their pattern has been stored in the buffers. (DW: Voyage of the Damned)
Teleportation when power is low can result in an incomplete transfer causing part of units to not materialise. (TDA: The Pirate Loop)
Sontarans had to use pods at areas for dematerialization and rematerialization. (DW: The Sontaran Strategem / The Poison Sky)
Captain Jack Harkness's Time Agent Wrist Strap contianed a teleport as well. The Doctor, Martha and Jack used it to teleport to the Valiant and <artha later used it to escape the Master to Earth. It was taken from her by him later and he teleported to Earth with it to try to force the Doctor to stop, but the Doctor called his bluff and later teleported them back to the ship. The Doctor deactivated the wrist strap's ability to teleport and travel through time, but Jack was able to re-initalize the teleport function with a missing bit of information gleaned through Project Indigo thanks to Martha. Jack then teleported with it to the Doctor and the TARDIS.
UNIT created Project Indigo using Sontaaran technology to create a teleporter of their own. Martha Jones managed to use this experimetnal teleporter to escape UNIT's headquaters when the Daleks attacked and was able to use part of the code in it to help Captain Jack bring his own teleport back online.