Space travel

Space travel was travel from one celestial body to another.

Development of the ability to travel through space was regarded as one of the first real steps species took in their planetary and species' development. The Time Lords developed space travel when "the universe was half its present size." (TV: Genesis of the Daleks) Humanity's first sojourn into exploring space began in the mid-20th century with the launch of several satellites. (PROSE: Alien Bodies)

Methods
For most species vacuum was an extremely hostile environment. Therefore, to travel to other world they needed to find a way of avoiding exposure to it. The most common way was building spacecraft. Mankind has learned it by mid-20th century. (TV: Day of the Moon); other species did it billions of years before. (TV: City of Death)

Some planets, including the Earth in the late 21st century, had space elevators, allowing the inhabitants to access the orbit.(TV: The Waters of Mars)

A faster but more difficult method was teleportation - direct transmission from one place to another, whether by technological (TV: The End of the World, Boom Town, The Time Monster) or supernatural (TV: The Brain of Morbius) means. The Kitlings were able to teleport by willpower. (TV: Survival)

Biological abilities
Some species had a native ability to move through space, like star whales (TV: The Beast Below). Wirrn (TV: The Ark in Space), Rutan Hosts (PROSE: Shakedown) and the Eight Legs (TV: Planet of the Spiders) were also able to travel through space without any technology.

Some species such as Time Lords could survive for a time in the vacuum of space, though they still needed to breathe oxygen. (TV: Four to Doomsday, The Doctor, the Widow and the Wardrobe)