The production of maps by PCs in the fictional world is an under-used adventure goal despite its dramatic potential. "Surveyor" is actually one of my favourite PC occupations - I've played four in various eras and settings in my roleplaying career. Surveying is the oldest licensed profession in the world (the Romans issued licenses for it), found in almost all sedentary civilisations, and the basic techniques have been intact for thousands of years. Though aerial photography has allowed better information, a surprising number of the processes involved in field surveying are simply refined versions of ancient ones.
One reason for the under-use of surveying and mapmaking as adventure goals is that most people are not surveyors or cartographers and therefore know little about what goes into producing the information that creates an accurate map. This leaves the process abstracted and therefore uninteresting.
First, watch this video in three parts    by the United States Army about how maps are made (circa 1973). This explains the basics of triangulation, using plumb lines, theodolites, chains and tapes, plotting tables etc. There are some references to modern technology (an ancient surveyor would use a dioptra, not a theodolite; obviously planes with cameras don't exist in most fantasy settings) but ancient, medieval and early modern tools include the alidade, groma, astrolabe, clinometers (basically variations on astrolabes in their earliest versions), quadrants, sextants, and of course compasses, rulers, telescopes and measuring rods which gathered similar information to the newer tools.
The basic technique in surveying is determining the distance between three points, known as triangulation. So long as one knows the length of one side of the triangle and the angle of the lines from two of the points to the third, one can calculate the length of the lines and therefore the position of the third point, as well as the area of the triangle, using trigonometry. Most of the tools mentioned above help perform one of the two functions. A chain or tape is used to fix the length of the known side, while tools like dioptras are used to measure the angle of the lines forming the triangle. Because this process relies on sighting the third point, various workarounds exist for where terrain prevent clear sighting (i.e. a forest, intervening mountain, etc.), like the construction of towers. All of this happens in three dimensions, not two, so there are additional calculations to determine the relative heights of the points and how that affects the calculated lengths of the lines.
A web of interlocking notional triangles is created by surveyors hopping from point to point until the relevant area is covered. A single hexagon can be split into six equilateral triangles, for those hoping to use this with hex maps, though most map hexes are too large to be mapped that simply.
If you want to get an idea of the challenges that crop up while surveying, it's worth reading Mason and Dixon by Thomas Pynchon, which along with being a really great book goes into a lot of detail about how difficult a surveying project can be logistically. PCs who want to execute surveys will have to frequently split up for extended periods of time with one party tromping around in the woods or up hills to place markers, while others go to set up the sighting equipment. You'll need teams of people to cut down intervening obstacles like trees, some way to signal between the parties so they know when the other team is in place or when the task is completed, maybe a building crew plus a stock of building materials to knock up sighting towers when you need them, someone to build and set markers on the points you locate, etc. Plus money for this crew, and guards to keep order, and handlers for all the baggage, etc. You might even need a mathematician. And don't forget the cartographer, the guy who makes the actual maps.
Part 2 of this will deal with cartography, which is the translation of the data gathered during surveying into maps and related representations.