I mean although Star Trek said that their ships travelled faster than light, they never actually explained how it was done. Instead, they added the terms 'warp core' to tell how FTL (which consume lots of energy) is sustained. They added the term 'dylithium matrix' to explain how they managed to control the warp phenomenon. The added 'warp bubble' when they realized that Einstein's Theory of Relativity forbids FTL, that pretty much meant that everyone travelling at Warp 8 will regress into babies within a few minutes. When they found out that teleporter technology was impossible, they added 'heisenburg compensator'. When they found out that at that speed, everything alive will liquify against the wall, they created 'inertial dampeners'. Warp drive in Star Trek is basically similar to punching your spaceship at super FTL speed through space, protected by a 'warp bubble' that keeps the people inside from getting younger. That means it's entirely possible for the spaceship to hit celestial bodies, like planets, asteroids, other ships or be affected by solar winds. That's why the created the concept of 'navigational deflectors', to keep the ship safe on its FTL journey. Because at that speed, being hit by an iron asteroid the size of a basketball will punch a very big hole in a starship.

Andromeda by Gene Roddenberry (creator of ST: TOS) does not believe in FTL at all. Their FTL involved using a living being's instincts to find a path among the twisting tendrils of subspace tunnel that connected every single world and system within the three galaxies. Though they do have an FTL ship in one episode, the Bellerophon, created before humanity were given the 'slipstream' technology that 'runs like a wild horse'.

Battlestar Galactica doesn't use FTL either. They do use 'jump drive' which allowed them to fold space allowing instantenous travel between one point to the other. In a way, one can say they're FTL, but not FTL at the same time.

The concept of jump drive is also shared between other sci-fi movies and shows, simply because it doesn't trample on Einstein's Theory of Relativity, unlike Star Trek. Star Trek trampled everything, even itself.

The movie Event Horizon also uses the concept of jump drive. However, there was a mistake somewhere and instead of jumping into another point in space, they jumped into Hell.

Many other sci-fi, such as Stargate, Babylon 5 and Starship Troopers uses hyperdrive, a method where they punch through into another dimension which uses a different set of rules from the primary space, thus allowing them to circumnavigate Einstein's Theory of Relativity without trampling it. Later in Babylon 5 story, they invented the quantum drive, which allowed them to punch through into a deeper hyperspace, allowing much faster travel. The Vorlon invented the method of travelling into 'Third Space' which supposedly would allow them to travel faster, but unfortunately, the "Third Space' is populated by evil creatures. The concept of hyperspace is often described as considering space as a globe. Normal space travel is similar to us walking on the globe's surface. Faster engines only described as running or taking a car. Hyperspace is like tunneling through the globe to each the other side in a straight line, considerably reducing travel speed.

Other sci-fis such as Space, Above and Beyond uses natural wormholes. These doesn't trample on Einstein's Theory of Relativity, they use a different (real) theory altogether. However, these have the limitation of not being able to strike anytime they want to and have to wait for a wormhole to open before they can reach faraway places. The enemy does have the technology to force open a wormhole however, which gave them a tactical advantage.

The primary mode of travel in Stargate is the Stargate Network, a kind of theoretical device that allows the creation of wormholes between two separate 'gates'. The theory of a stargate is accepted as sound, but flawed and we do not have the materials nor the knowledge to actually create it yet.

Or you can just use the concept of 'sleeper ships' if time isn't an urgency. Basically it's a kind of spaceship that travels slowly, without FTL and have its crew asleep most of the time, relying mostly on the computer to find a suitable planet for colonization. This was a concept used in Firefly and Serenity, as their spaceships don't use FTL.

Prometheus and starships in Aliens also use sleeper ships, though their sleeper ships have FTL. The reason for them having to use sleeper pods is because in their universe, living beings can't survive the FTL.

As you can see, all these are theoretical. You don't have to explain everything. You just need to know what you want to do and make it believeable. Before Stargate (the movie), nobody thought that you can travel to another planet using circular stones. You just need to have creativity, or just tweak an existing method if you can't think of any. I'm using a new technique called quantum tunneling in one of my sci-fi books, which hasn't been continued for some time now. I can explain it, but if asked for technicalities or calculations, I won't be able to answer.

Hope this helps.