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Starships had several methods of traversing the great distances between points of travel. Faster-than-light travel was a common method.
Hyperspace often required significant power. (TV: The Stones of Blood) By the 30th century, several species such as humans and Hith were experimenting with different methods of utilising Icarons for use in spaceship design with regards to hyperspace. (PROSE: Original Sin)
As early as 4 billion BC, the Jagaroth had utilised warp drive as a method of propulsion. (TV: City of Death) By the 26th century, human spaceships utilising anti-matter were propelled using warp drive. (TV: Earthshock, The Girl in the Fireplace)
All Speed Inter-System Type Ks were a type of starship engine used by some Sycorax tribes. (PROSE: The Visual Dictionary [+]Andrew Darling, Kerrie Dougherty, David John and Simon Beecroft, Dorling Kindersley (2007). Page 94; Edition: 2014 reprint., The Coldest War: Marker 47 [+]Colin Brake, Decide Your Destiny (BBC Children's Books, 2010).)
Cryogenics[]
Rather than using faster-than-light or other methods of propulsion, some starships used suspended animation and/or cryogenic suspension to prevent their crew from ageing or experiencing the voyage. (COMIC: Profits of Doom!)