In Brogue, it appears that searching is not limited to just adjacent squares, but rather it affects a fair distance around you - perhaps even the entire room as your eyes can see. As such, discovering hidden doors and traps is a lot easier. You can search a few (4-6) times in the center of a room or corridor and you should be able to find anything without error.
Secret doors are pretty easy to know where to look for, especially due to the advantages of a long range search. There's two key things to take in mind. First, the path between the stairs is always possible without crossing chasms, lava, or deep water. If it ever appears that your only way to progress needs a potion of levitation or other method of crossing, look instead for ways that may have secret doors. There is guaranteed to be one somewhere. Second, Brogue uses up as much of each floor's allotted space as possible for rooms and corridors. Not unlike how one seeks things out in other Rogue-likes, always keep an eye out for dead space in your map - it's very frequently going to contain a secret room.
Traps are a bit more difficult. Note that traps are far more infrequent in the early levels of the Dungeons of Doom, while they increase in frequency drastically as you approach the bottom levels. Traps will not spawn on the likes of water and mud, but they can spawn on grass. Keep this in mind, especially when you reach the levels that incendiary traps are generated, as a flaming lawn can easily spell your demise.
If you're lucky, a very helpful trinket is the ring of awareness. This performs automatic searching in the area around you every turn. Again, as search affects an area around you, this is incredibly potent (as long as you don't have more combat-necessary rings to use). While higher enchantment levels improve the search accuracy of the ring, it would be wise to keep your scrolls of enchantment for other items.
Overall, the search intensity of Brogue is far less than that of other Roguelikes. The expanded range of search greatly helps, but also the number of secret doors is not nearly as large as in other Roguelikes.