How does vision work in nethack?

Your vision is based on the amount of light in the area. Most rooms are fully lit, so you can see the entirety of it. The same goes for most levels of the Gnomish Mines for example.

Corridors are not lit, which means you can only see one block in any direction. One exception is infravision, which is an intrinsic for dwarves, elves, gnomes, and orcs, allowing you to see infravisible (warm-blooded) monsters from afar, even in dark places.

As for the map, you recall the way things were the last time you saw them. If something happens to them but you're not around to see it, you obviously don't know of it. You will only see the change once you get within sight again.

Supplementing the accepted answer, adding light to your immediate vicinity (such as with a lit lamp, or a light spell) will enable you to see further into the dark (such as in corridors).

Also telepathy works similar to infravision. Extrinsic will allow you to see any monster in a certain radius that is not mindless. Intrinsic is similar, but only works wile blind.

Searching is done to detect hidden things, like hidden doors. Technically, these are visible, but you don't know that it's a door. Personally, I imagine a secret passageway-type door that looks like it's part of the wall, only upon close examination does it become apparent that it's a door.

Usually, if you're blind, you can't see anything. Otherwise:

• You can see immediately adjacent tiles.
• You can see lit tiles, if you have a line of sight to them. Some rooms are already fully lit (most of them in the early dungeon, but fewer later on), and most corridors are unlit.
• There are tools and spells that provide light — for example, a lit oil lamp creates a small field of light that moves with you, while a spell or scroll of light creates a permanent field of light around the position where it was cast.
• Infravision lets you see warm-blooded monsters even if they're on a dark tile, but they still have to be in your line of sight.
• There is an artifact that provides "astral vision", which breaks most of the usual rules, letting you see to a short distance even on the other side of a wall or door, even if it's dark, and even if you are blind.
• Sometimes monsters are invisible, and can't be seen except by players who can "see invisible". If you "see invisible" then it's as if the monster was visible — you can see it if the other rules say you can.
• Hidden/secret things might not be seen, even if they're visible. Until you find them, they appear as something else (usually a wall or a floor tile). Searching lets you find secret doors and passages, hidden monsters, and traps. You can also discover a hidden monster when it attacks you, or a trap when you blunder into it.

There are several abilities and items that will reveal the locations of items and monsters without relying on your ability to see, but naturally they don't fall under the rules for vision.