Science Fiction has a long tradition of people travelling through time. These can involve one-way and two-way travel, machines, physical states, vortexes, and even magic potions. Sometimes only the consciousness travels. Here are some of the mechanisms, and some key examples:
Energy source: seems to be electricity (batteries) only.
Science explanation: none given. It is difficult to understand what Wells had in mind with a rotating wheel, but may have been inspired by the elegant, if frighteningly impractical, penny farthing bicycles of his time. However, one tends to think there may be one or two technological steps between the bike and time travel.
Problems: how would the time traveller hope to recharge his batteries for the return trip? The far future world would not have the same environmental conditions, especially after having such a violent intervening period. Hence, the atmosphere would most likely not be breathable. Genetic mutation due to physical environment separation is the explanation for the two species, the morlocks evolving into mole-beings for living underground. But why do the surface humans so far in the future still look like the homo sapiens of today.
Back to the Future: Marty and Doc Brown drive a car (and in the second film a train) at high speed with a high energy source sending them into the past or future.
Energy source: plutonium in the first trip, replaced by electricity from a lightning bolt to return.
Science explanation: The time paradox was handled as a major theme by Doc Brown insisting Marty not change anything. Instead, Marty risks changing his family's history by preventing his father and mother falling in love. When he intervenes in key events of the past, members of his family in a photograph begin to disappear. In the second film, a future Bif brings an almanac back to 1955, and gives it to the young Bif, so he can use the information to make a fortune. This creates a parallel future 1985, a dystopia which Marty has to revert by preventing Bif from keeping the almanac in 1955.
Problems: although good for the drama value, the plot does not explain how Marty could know about the alternative future scenario if Bif uses the almanac. Parallel timelines does not resolve this enigma, since Marty travels to and from the same 1985.
How could any machine be able to change fuels from plutonium to electricity so easily?
The secret of time travel is related to Doc Brown's invention, discovered when something fell on his head in the bathroom, the 'flux capacitor'. No explanation is given about how this is supposed to work, but it sounds good.
Planet of the Apes. Time dilation by travelling in a space ship very fast, so that the astronaut experiences the passage of time much slower than the people on Earth.
Energy Source: not specified, but possible an ionic drive, firing ions at close to the speed of light out the back of the spacecraft would cause it to accelerate, although possibly not to the 99% of the speed of light they would need to achieve a 2,000 year jump in time.
Problems: the humans look suspiciously like Californian university students in rags. If the environment had changed so much as to cause the dramatic change in landscape we see at the end of the film, then there would presumably have been physiological changes to the humans as well as the champanzees.
Why did humans lose speech, and grow less intelligent, and yet survive as a species at all? For that matter, why are the apes 'ape-ing' humans? Same social hierarchy, language, same military and religious nutcases and their dogma...
Relativity was also used in Star Trek to travel back in time and save the whales.
For more information about Relativity, see: Time in Fact
Les Visiteurs, 1993. The knight, Godefroy, Count of Appremont and Papincourt, asks the wizard Eusebius to send him and his servant, Jacquouille la Fripouille, back in time to undo a tragic mistake caused by sorcery. The wizard gives them a magic potion to drink, which reduces them to piles of manure, before they travel 700 years into the future by mistake. They reverse the journey at the end of the film to change the events of the past as they intended originally.
Another popular time travel mechanism is that of consciousness only travel.
In the novel Vitruvian Boy, Sean Seulpierre doesn't physically travel in time, but his consciousness replaces that of others living in another time. The novel uses modern physics to explain the relationship between time, space and matter, and how memory is necessary for perceiving a timeline.
A further example is the X-Men movie Days of Future Past. Some time in the future, a mutant uses her powers to project Wolverine's consciousness back into his former self, in 1973.
A similar mechanism is seen in the film Terminator: Salvation, this time to the future. In 2003, death-row inmate Marcus Wright is convinced to hand his body over to scientific research after his execution. He then finds himself in 2018, with his consciousness grafted into a robotic body, seemingly identical to his own: from his perspective, he has time-travelled 15 years.
In the 2011 film Thor, the denizens of Asgard use the Bifröst bridge to travel between their world and the nine realms, one of which seems to include Greenwich.>
Scientific basis: This concept is similar to the proposal by Albert Einstein and Nathan Rosen that it may be possible to travel across the cosmos and time via wormholes.
For more information about the ER (Einstein-Rosen) wormhole, see: Time in Fact
Star Trek. Spock travels to the past via a Black Hole to a parallel universe and warns Kirk of imminent danger.
Dr. Who in the TARDIS (time and range dimension in space) simultaneously jumps in space and time by the huge amounts of energy the TARDIS can focus into dimensional distortion.
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