The X Rebirth game is set within a fractal-like network of Zones, Sectors and [solar] Systems that are all within, so far, one Galaxy. There are multiple Zones within each Sector, and there are multiple Sectors within each System. There are different means of travel for different types of location, which are described below. There's a great-looking map here.
The beta version of Rebirth v4.00 contains changes to the dynamics below for the player ship (the Skunk) as a player ship jump drive is being introduced. However, since things can change before release, this guide focuses on the v3.61 game world for now but it is technically accurate in the beta 4.00 anyway.
Free-flight within sectors
Within a sector all ships can freely fly around within and between zones. While we are between zones, we are in "empty space" but if we wish, we can create a permanent new zone on those locations by dropping a nav beacon or building a station there; the latter allows us to rename the zone if we like and claim our own little home 
Small and Medium (S/M) ships, which include the Skunk, can fly at regular speeds or use their boost engines to temporarily speed up. The Skunk's boosted speed is faster than other ships but it depletes shields as a tradeoff. In general, S/M ships will tend to take regular highways (see below) between zones but at other times they may boost, particularly in short bursts while attacking. Large and Extra Large (L/XL) ships (AKA capital ships) use free-flight within zones and boosters between zones; they are unable to use regular highways.
As ships increase in size between S to XL their speeds and turning rates tend to decrease, so within a given zone small ships tend to reach their destinations quickest. However if a ship needs to travel between a few widely-spaced zones, capital ships tend to be quicker since although they are slower than S/M ships, their booster can save time as it can operate continuously and the ship flies directly to its destination rather than sticking to the highway route.
Regular highways within sectors
S/M ships, including the Skunk, may use regular highways to travel at a faster speed between zones. These features look like long, mist-filled, cylinders where the flow of the mist indicates the direction a of travel. Different highways may have different rates of acceleration to each other and along sections of highway, acceleration rates may vary too. Using boost in a highway increases the Skunk's acceleration rate.
In order to use a highway, we only need to fly into them and after which, the Skunk moves to the centre lane and begins to accelerate. We can control our speed and position within the highway at all times and the Skunk will stay within a given lane regardless of the shape of the highway. The easiest way to maneuver within a highway as a keyboard user is to press the space key to activate the cursor and then to use the arrow keys to change 'lanes' if wanting to dodge slower NPCs (crashing into them will force their exit & slow you down). In order to exit a highway at any time, press the backspace key (not sure about joysticks/pads). Repeatedly crashing against the sides will slow you down and probably eject you, whilst shooting other ships can force them to exit. <Note - the outside of the highway lanes tend to be the fastest due to less traffic, but it's fairly easy to exit by accident - Snafu>
Regular highways are similar to Super highways, which allow S/M ships to travel between sectors (see below). Both regular and super highways are unidirectional, although they're often located near entrances to routes going in the opposite direction. Some sectors have relatively direct highway routes between their zones whilst others can meander around a bit. Either way, apart from within Radiant Heaven sector and the Teladi Outpost DLC sectors, the highway network typically offers the quickest route between zones for S/M ships.
Super highways between sectors
Super highways are pretty similar to regular highways. Only S/M ships can use them and they are tubes that connect different locations (sectors rather than zones). The main differences are that they cannot be voluntarily exited before reaching their end and there are occasional fiery obstacles that slow the Skunk and/or drain shields unless dodged.
Jumping between sectors by capital ships
This is the method that L/XL ships use to travel between sectors. In order to do so, they use their jump drives to jump to a Jump Beacon in a neighbouring sector (e.g. a second sector that is connected to the starting sector by a super highway). Therefore if may be necessary for a capital to make multiple jumps when travelling from point A to point B within the same system, but in any case it is typically a faster means of travel than for S/M ships flying to and through super highways. Undertaking multiple jumps requires a charge-up period before each one, which jump fuel dramatically speeds up. Capital ship captains have a setting that allows them to automatically make refuelling trips to Cell Recharge stations if they need to make a jump with less than 400 cells. Since jump fuel is relatively cheap, it makes sense to leave this active rather than force the capital ship to make free, but protracted, jumps.
Travel between systems
This can only be achieved via Jump Gates, which require approach and flying through via free-flight (see above). So far, each system has at least 2 gates but some are inactive. Of the inactive ones, some are not in use by the game [yet] and some connect to the Teladi Fields of Opportunity system ("The Teladi Outpost" downloadable content (DLC)) - a trend that may continue with recent the announcement of a new DLC that is anticipated to arrive with or around the upcoming release of 4.00. Once a gate has been traversed, the ship will find itself within a new zone and from there, may continue on its way via the methods described above.
Additional info
For further info on how the game engine treats different locations depending on whether the player is nearby or not, please see this page.