Time travel

Time travel was, as the name suggested, the (usually controlled) process of travelling through time, even in a non-linear direction. In the 26th century individuals who time travelled were sometimes known as persons of meta-temporal displacement. (PROSE: The Mary-Sue Extrusion) According to the Eleventh Doctor, "Time travel is damage. It's like a tear in the fabric of reality." (TV: The Name of the Doctor)

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The Doctor's TARDIS travels through the Time Vortex.

Methods

Technological or biotechnological methods

By space-time vessel

Time travel of this kind commonly required a great deal of power. The Time Lords converted a star into a black hole. This produced a wormhole to achieve time travel (TV: The Three Doctors). They used the Eye of Harmony thereafter. (TV: The Deadly Assassin) Following the (presumed) loss of the Eye of Harmony, the Ninth Doctor used the Cardiff rift to "re-charge" his TARDIS. (TV: Boom Town)
The Third Zone scientists Kartz and Reimer built a primitive time machine modelled on Time Lord technology. It almost worked, but ultimately only made one successful trip before it was destroyed. (TV: The Two Doctors)
Magnus Greel used an experimental time cabinet based on 51st century human technology. (TV: The Talons of Weng-Chiang)
The Imperial Daleks under Davros, who already had limited time travel technology, expected to do the same. (TV: Remembrance of the Daleks)

Travel using time vessel commonly involves the Time Vortex.

Other technological means

Osmic projection was a means of time travel used by the Sontarans. The Third Doctor referred to it as rather limited in its temporal range when used by the Sontaran scout. (TV: The Time Warrior)
Time Scoop technology enabled the user to transport other people and objects remotely. Without any ally on the other end, it could leave the user stranded in another time period with no way to return. (TV: Carnival of Monsters)
Time corridor technology was used by the Daleks, (TV: The Evil of the Daleks, Resurrection of the Daleks, Remembrance of the Daleks, Victory of the Daleks) Osirians, (TV: Pyramids of Mars) the Borad (TV: Timelash) and the Ra'ra'vis. (COMIC: Time Fraud)
A kind of time viewer, called a quantum imager, enabled one to observe and (to a limited degree) communicate with people in the past. (PROSE: The Least Important Man)
Pushing energy into warp drive could create a time window. (TV: The Girl in the Fireplace)

A warp drive accident fractured one unfortunate individual, Scaroth, into "fragments" scattered through various eras of time and linked by telepathy. (TV: City of Death) Another warp drive accident had the effect of propelling the vehicle in question roughly sixty-five million years back in time. (TV: Earthshock)

A rift manipulator could be used in conjunction with the temporal rift itself. (TV: Captain Jack Harkness, End of Days)

The column in the centre of a human-built rift manipulator looked like the central column a TARDIS, indicating, perhaps, a similar function.

A vortex manipulator was a crude time travel device. It could miss by hundreds of years and broke down easily. It was referred to by the Tenth Doctor as more of a "space hopper" compared to the TARDIS. One was later used by River Song and the Eleventh Doctor after the TARDIS exploded in June 2010. (TV: Utopia/The Sound of Drums, The Pandorica Opens/The Big Bang)
Emergency temporal shift was a form of time travel used by the Cult of Skaro to escape being sucked into the Void and was later used by Dalek Caan to escape from 1930s New York. (TV Doomsday, Evolution of the Daleks)

Mirrors

Time travel by use of mirrors was based on the principle that mirrors reflect light and time travel is moving faster than light. If static electricity was passed through the mirrors, more than images could be reflected and whole objects could be sent back in time. As well, certain trace elements in the machine, like taranium, were also needed. (PROSE: The Wheel of Ice)

Edward Waterfield and Theodore Maxtible attracted the attention of the Daleks while experimenting with static electricity and mirrors. (TV: The Evil of the Daleks)
The mysterious Gateway situated in the void between N-Space and E-Space provided access to different times and realities, sometimes through mirrors. The exact process remains unknown. (TV: Warriors' Gate)
General Mariah Learman and Professor Osric succeeded briefly in making a functioning time machine with over 100 clocks and 1000 mirrors in her prime ministerial house. The act of measuring time changed time and therefore time could be manipulated. The mirrors were coated in Orthopositronium, a material where the positron and the electron orbited each other in the same direction. It briefly worked when the Daleks ship ran aground in the Time Vortex and they homed in on it and made it work. It needed Chronons to work, which were sourced when the Eighth Doctor's companion, Charley, held the master clock. It took her and Viola Learman to Shakespeare's time. This ceased to function when Charley entered the Doctor's TARDIS. (AUDIO: The Time of the Daleks)
A time machine was created by UNIT with the help of Rose Tyler and the dying TARDIS to send Donna Noble back to her own timeline from a universe the time beetle created. (TV: Turn Left)
The Arkive tried to create a mirror-based time machine, but didn't have the necessary parts or skills to make it. (PROSE: The Wheel of Ice)

By psychic power or other natural ability

The Eight Legs could teleport as easily through time as through space. K'anpo Rimpoche, a highly advanced Time Lord with great mental discipline, could do the same. (TV: Planet of the Spiders)
The enigmatic Bilis Manger could also also teleport at will through both time and space. This ability was only seen in the vicinity of the Cardiff Rift however, and so could have been linked to it in some way.(TV: Captain Jack Harkness, End of Days)
Transcendental Beings had free movement through space and time.
Fenric could transport other living beings via time storms. The people displaced by the time storm often believed they had caused the time storm themselves. (TV: Dragonfire, Silver Nemesis, The Curse of Fenric)
The Fairies could travel through time and space naturally. (TV: Small Worlds)
The Weeping Angels had the ability to send others back in time with a touch. (TV: Blink)
The Trickster, prior to manifesting as a corporeal being, could traverse time and space with ease, though not at any given moment. (TV: Whatever Happened to Sarah Jane?, The Temptation of Sarah Jane Smith)
The Androzani trees travelled through the Time Vortex by using Madge Arwell as a host. (TV: The Doctor, the Widow and the Wardrobe)

By space-time anomaly

The Tharils "rode the time winds". (TV: Warriors' Gate)
A warp ellipse could possibly make time travel possible. (TV: Mawdryn Undead)
Travel via time rift was possible. The Weevils arrived on Earth via this method (TV: Everything Changes), as did a human aircraft, the Sky Gypsy. (TV: Out of Time). During rare "negative spikes", the Rift also occasionally abducted random people in time and space from Earth, and disastrously attempted to correct itself. (TV: Adrift).
Sarah Jane Smith acquired an alien/futuristic Time Converter which allowed her to open and close time fissures, but these usually only linked two particular places in time. (TV: The Temptation of Sarah Jane Smith)

Taking "the slow path"

Some individuals, by necessity, sought to take what the Tenth Doctor once described as "the slow path," (TV: The Girl in the Fireplace) spending hundreds or thousands of years patiently waiting to return to a desired time. (PROSE: Birthright) A less arduous method would involve cryogenics or some other form of life suspension.