Since we in Incudea -and Belklaun as a whole- rely so much on the number six, our cardinal direction system is a bit different from yours. We're also probably more used to speaking of and using three coordinates, since we've been out and about in space for so long. The common layperson's breakdown of directions follows the following diagram:
The differences with Earth's are easy to see. Your cultures most often speak of four cardinal directions: North, South, East and West, with secondary directions between them. Some of your cultures have 8 basic directions instead. The universal practice in Incudea is to use not 4 or 8 but 6 basic directions, with your West and East replaced by Northwest, Southwest, Northeast, Southeast. We do have abbreviated compounds for West and East specifically (sorro, fodo) but they're not really necessary. If you need to fine-tune these directions, you can simply opt for the closest line available to you. Once you start doing systematically, especially within the context of an occupation, you start thinking of directions as bands instead of pure lines. The clocks below show a scheme used often by the Inculae (the clock format should help you see things better I think).
For now let's just focus on the left clock, which handles two-dimensional space (x,y) like the land we walk on. For more precision, each direction is broken into three equally-sized sections. The middle section is always called Pure (sain), counterclockwise from Pure is Ei (in reference to the first trinity world Aym or Eim) and clockwise is Cho (short for Chanegra). Thus, using the times on the clock for reference: the direction at 11:00 to 11:40 is termed Ei North (ei paiduin), 11:40 to 12:20 is Pure North, and 12:20 to 1:00 is Cho North. 3:00-3:40 would be what then?
If you guessed Ei Southeast, you'd be right! You're probably already wondering: what happens if the direction is exactly 1:00 then? Is it North or Northeast? The norm, not followed by some, is to say it's North-Northeast (compounding the two directions in a clockwise manner). I might as well add here that another scheme is to mix lines and bands for the directions: most often, North and South are considered lines, splitting the clock as it were. Then the left side of the clock is split evenly between bands of Northwest and Southwest, and the right side between Northeast and Southeast bands. This for all intents and purposes 4-direction scheme is favored by Zeburajas, Maras and others (though my understanding is that Maras rotate their clock; there is some variation even within specific systems).
Now, once we move on to three-dimensional space, we need to introduce the second clock. Starting from the position of the first, rotate the second 90 degrees to the right (in the Y axis) and then 90 degrees counterclockwise (in the X axis). In the diagram above, I've represented this latter aspect by rotating the colors. Note that even though on the first clock, x is positive toward the right, on the right clock, z is positive toward the left. (y is positive upwards in both clocks.)
We do not have actual proper words in Horgothic to refer to these second set of directions, so each species uses different terminology. We Inculae have devised portmanteau words derived of prol and hel (front and back), and jein and vuk (up and down) plus the word for direction (ando). I've been forced here to coin some words in English, the key ones being "frest" (front+west) and "beast" (back+east). Notice how the pure positive y direction in the first clock, original North, points at 12 (ruling over the yellow band), whereas the pure positive z direction in th second clock, Frest, points at 9 (ruling over the yellow band again). This is the 90 degree rotation I was talking about. I think it's easy to decipher the other directions in the second clock: Beastown is Beast+Down etc. This second clock is used in conjunction with the first to specify directions in three-dimensional space. For example, the planets Dani and Danaton are said to be northeast-frestup from the Home System. Incidentally, we also like to make a distinction -really a relic from older times- between the North and the South of the universe, i.e. between stars with coordinates (x,+,y) and those with (x,-,y), where (0,0,0) is defined as the location of the Home System. We don't ever really talk of the Frest of the universe and the Beast of the universe, and even less of similar distinctions in the x-plane.
When talking two-dimensionally, we always only use the terms in the first clock. That said, some species will borrow terms for the second clock to fill in the first. Glapachikos, for example, will use their equivalents for Frest and Beast to speak of West and East on land and sea. (Glapachikos are not the most sophisticated of nations, so beware.)
Alas, having said all of the preceding, these clocks don't really cut it when we need to talk about directions with more precision. For scientific and military matters, we usually go with degrees. We divide the circles or clocks above into 36 degrees (topion). For historical reasons, we use 3 o'clock as the 0 degree line. 6 is 9 degrees, 9 is 18 degrees, etc. For even more precision, each degree is subdivided into subdegrees, and so forth. When we bring in the second clock for 3d space, the 0 line is o'clock, and as expected the angles open clockwise, with 3:00 being 9 degrees. We will then speak of a star's position relative to a ship by citing two angles, the one for the left "clock" and the one for the "right" clock. We often use a 36 number set when speaking of these matters, so the description is nice and concise: to use the standard Human base-36 system (numbers 0-9 and the letters A-Z for numbers 10-35), the star could lie in the B4 direction.
Here's a more concrete example. The Aurena Green System lies on coordinates (x=-34,y=1,z=36) in Darkion miles, rounded. Say we're on a ship located coordinates (22,4,40). In what direction should we set course to reach Aurena Green? The clocks below give the result of 1.4 and 14.3 degrees. What we have done is take the angle from the degree zero line (3 o'clock for the first clock, 12 o'clock for the right clock) and make a sweep until we reach the line between the two points in question: in this case our ship and Aurena Green. And yes, it is easier to set course for Aurena Green using the planet's coordinates and be done with it. But the degree method has its uses, for example, when giving a general direction rather than a specific location, and also when firing certain weapons. Speaking very roughly, this 1 degree and 14 degree combination could be represented in base-36 as 1E (in Horgothic, shen-lon.