The best way is to use a map and compass. But if neither are available if you are the first to explore, and map the planet, for instance, here is some info you will need to know.
The directions; north, south, east, and west, as we know them are fairly useless. They are not constant for other planets, or astral bodies. They are simple names for polar north, polar south, turnwise (east), and widdershins (west) on earth. Though north, south, east, and west are the original names, they don’t mean much off earth.
The alignment of the poles may be inverted on other planets, with north being on bottom, and south on top. Yes, I know that top and bottom don’t mean anything in space, nor do north and south, but I’m sure you understand my meaning.
East and west are not the same for planets rotation. Neither are clockwise or counterclockwise. Turnwise (the direction of planets rotation) and widdershins, are more appropriate, since all the planets turn. If a planet doesn’t turn then night or day would be a full trip around the sun(s).
For the sake of this write up “normal” astral bodies are roundworlds. Ovular (earth), spheres, and Dyson spheres. True, it is hard to consider a Dyson sphere to be normal, but navigation follows the same rules as for the two other examples, however the mapping deformations of the inside of the sphere are opposite of the others. Also a Dimple sphere is only a Dyson sphere variant, so they won’t be covered.
Discworld
Consider a planet that is only a flat disc or plate. There is a axis but it is the center, or hub of the planet, so polar directions don’t work. The best navigational points you would have are the hub, or center, and the rim, or edge. I don’t know how you make a compass that points hubwards, or rimwards, unless one has a stronger magnetic pull.
Again east and west are not applicable; instead we turn too turnwise and widdershins. There are no hemispheres. If you are standing facing the hub of the planet, turnwise is in one direction, widdershins the other. However, if there is another person standing on the side opposite of the hub with their back to you, the directions would be opposite.
So, the primary map directions of a discworld are hubwards, rimwards, turnwise, and widdershins. Mapping a discworld is fairly straight forward. Since the planet is flat there are no map deformations to take into account, like those of a planet that is curved. There is also no horizon. If you wish to map the edge of a discworld you follow the same general rules as those for a ringworld.
Ringworld
The planet is simply a large loop floating in space. Turnwise and widdershins work fine for you. Hubwards and rimwards do not, because the entire planet is the rim. Polar directions would work if you had a magnetic pole, but you don’t. So, what you do is face turnwise or widdershins, and identify either your left or right to be north, south, top, bottom, squiggle, thumb, which ever you like. However, if you have two or more rings evenly bisecting, you can use the directions similar to roundworlds.
Mapping is similar to that of a roundworld, with map deformations. Just remember that the deformation pattern is opposite for the inside of the ring, and outside.
Faceted
By faceted, I mean geometric shapes. Rectangles, pyramids, any thing made up of flat sides. I’m not covering conical shapes. The minimum number of facets a world can have is four without the facets being curved.
Fortunately, map directions are basically the same as those for roundworlds. That is if you are lucky enough to find a world that is made up of an even number of facets greater than six, symmetrical, and with an axis connecting two opposite corners. If it is not symmetrical (being caused by an odd number of facets, or irregularly shaped facets), or the axis intersects the plane of any of the facets, there will be problems. If the axis intersect the plain at any point, then polar directions on that plane would be fairly useless, unless it is in the exact center of the facet. Turnwise and widdershins will work as you rotate around the pole, but be prepared to come up with new navigational methods.
Mapping is again simple because there are no map deformations on each facet, you can map each facet separately, though these may add up considerably if you have a large amount of facets.
Doubter has given me some more info:
"For your navigation node: earth is actually an oblate spheroid; one of the most logical shapes for a geometric world would be a truncated icosahedron (soccer ball) or a regular isocahedron (20 sides, all equilateral triangles)... :)"