Travel between star systems was a routine fact of life for most of the cultures Blake and his followers encountered. The vast majority of starships employed some variety of FTL (faster-than-light) drive, for example all the ships of the Federation, System, and independent human travellers.
It was the same for most alien civilisations, with a couple of exceptions. The capsule encountered by the Liberator en route to Saurian Major appeared designed to travel interstellar distances with the crew in cryogenic suspension. The Keezarn people had launched a ship, apparently at STL velocities, which would carry a teleport terminal to a new planet for them to colonise. (A: Time Squad)
How ships achieved FTL velocities was not revealed. While the London was fitted with a 'hyperdrive' and there were occasional references to hyperspace (Roj Blake mentioned hyperspace ships while Blake suggested the great speed of the Liberator might be a result of accessing negative hyperspace), ships were seen travelling in normal space - and the terminology involved suggests a degree of time dilation (experienced in normal space while experiencing a high degree of STL acceleration) being experienced. However Dayna only stated that it was impossible to achieve extremely high speeds (Time Distort 12, in this instance) in 'real time', suggesting that the actual distortion involved in use of most levels of Time Distort speed was negligible.
At standard cruising speed it took eight months for the London to travel from Earth to Cygnus Alpha. No other journeys appear to have taken anything like such a long time, at least from the viewpoint of the crews involved, with travel times most commonly measured in hours or days. Time seemed to pass at the same rate on planets and ships, further lessening the likelihood of time dilation being a factor.
It seems that travel between galaxies was not yet possible using existing Federation technology. On discovering the minefield beyond Star One on the galactic rim, Avon speculated that an intergalactic drive had been developed. The Andromedans almost certainly possessed such a drive. (B: Star One)
In "Horizon (episode)" Ro states that monopasium 239 is needed for the "hyperspace ships".
Time Distort was the standard measure of interstellar speed employed by the Federation, and possibly other human interests.
Federation pursuit ships prior to the Intergalactic War had a safe crusing speed of up to Time Distort 9, with at least some models equipped with an emergency maximum speed of Time Distort 10. (B: Hostage)
The Mark Two photonic stardrive could achieve the equivalent of Time Distort 15 in real time, a considerably greater speed than had previously been thought possible.
Zen measured speed in terms of the 'Standard' convention - i.e, Standard by One, Standard by Two, and so on. If 'Standard' refers to the standard cruising speed of the Liberator, then the crew routinely travelled around six times the ship's 'normal' velocity, perhaps explaining why Liberator's energy banks were prone to exhaustion. That said, Vila Restal stated that Liberator was able to "out-stroll" other Federation ships.
Even after transferring to the Scorpio, the crew continued to use the 'standard' convention - which means the measure would have to be modified given the poor acceleration of Scorpio at that time, or it may refer to some other constant. But given the great speed of the Liberator this is almost certainly some value exceeding the speed of light.
The maximum speed the Liberator could achieve safely was Standard by Twelve, although the other DSV-class ship launched by the System achieved Standard by Fourteen immediately prior to its destruction; other System vessels were similarly faster than Liberator. Blake once said that the crew would lose control of the ship at Standard by Twenty, suggesting greater speeds were achievable in the correct circumstances. (B: Redemption), (A: Breakdown)
At maximum speed, presumably Standard by Twelve, it would take Liberator several generations to reach Andromeda. In real life, the distance to that galaxy is well established as 2.5 million light years. This allows for the calculation of the speed of Liberator at Standard by Twelve as exceeding 30,000 times the speed of light. This speed would allow Liberator to cross the full diameter of our galaxy in 3 years. Other values of Standard speed are less known, as it is unclear if Standard speed is a linear or logarithmic measurement system. (B: Star One)
Converting between Time Distort and Standard speeds can be difficult, but not impossible. While evading a coordinated Federation space attack not long after Blake's first assault on Control on Earth, Liberator achieved a speed of Standard by Ten, at the same moment that the lead strike ship noted that Liberator was approaching Time Distort 20. This, combined with other measurements, suggests a ratio between a unit of Standard speed and a unit of Time Distort of somewhere between 2:1 to 3:2. (B: Hostage)
However, the Mark One photonic stardrive developed by Plaxton was calculated as having a top speed of over Standard by Twelve, with Plaxton and Atlan later stating that it had a top speed of Time Distort 12. This suggests that by this time the two systems were interchangable, or that Liberator's method of travel was not dissimilar to photonic flight (granting the ship an additional edge over pre-war Federation ships). (D: Stardrive)
It is also possible that 'Standard' speed varied from ship to ship.