Well, for myself, 9 out of 10 times when I arrive at the stream, there isn't a hatch in progress, so the trout are feeding opportunistically on whatever happens by their feeding or holding stations. They're not keyed in on one particular insect, nor are they showing themselves by rising to a hatch. A searching pattern can represent any generic "bug" that would tempt a trout into biting. You can either wade upstream or down, swimming or drifting your fly into potential lairs such as brush, undercut banks, in front of or behind obstructions such as boulders where trout like to hang out. These lairs provide them with concealment from predators and/or access to a steady stream of food.
Some other patterns that may be considered "searching" patterns could be the Hares Ear soft-hackle, the Prince nymph, or the Wooly Bugger. These patterns represent nothing in particular, but are representive of a generic "bug".