Nethack has secret passages (blocking corridors) and secret doors (embedded in room walls). You must find them before you can pass through them. The canonical way of discovery is searching, but it's not the only one. For example, if you're sure there's an hidden door in a certain square, you can try kicking it. If you're lucky you'll find the door, break it and gain some bonus experience points -- IIRC.
That's all good and fun, but where should you search?
Stairs always happen in rooms. Thus, you should look for "holes" in the map where a room could fit. If there are dead end corridors in that general direction you might be on the right path!
Here's a real life scenario. I marked some educated guesses with question marks to illustrate my point.
----- ------- ???????
|...| |.....| ? ?
|....###### |......# ? 3 ?
|{..| #......|# ? ?
----------- |...-#######-------# ???????
|..........#####|...| # ?
|.........| #-...| # ?
|`......<.-#####----- # ?
----------- ############## # ?
? ? #### ?
????????? ??????? #--|---?
? ? ? ? @|....|?
? 2 ? ? 1 ? #|....|?
? ? ? ? #.....|
????????? ??????? |....|
------
1
looks the most likely: a continuation of a dead end corridor. 2
is also plausible, that large area down there is so likely to have at least two rooms. 3
looks more far fetched, but it's exactly where the hidden door was.
I hope this still gives you an idea of how to make reasonable guesses when looking for secret passages.
Oh, and remember to never ever hold a key when playing Nethack. One search is hardly going to be enough, so run the search command multiple times the right, safe way: 20s (020s if you have numpad on) will search the current position for 20 times only if it is safe enough to do so. Hunger, approaching monsters and the like will abort your search, unlike holding a key does.