Characters can search for 1 AP per search. The button for searching (labelled "Search") can be found in the "Basic Actions" pane. Each time a character searches, there is a chance of finding an item, a hidden character if one is present, both, or neither. This chance is independent of previous attempts. Just because the last search didn't find anything doesn't mean that the next search attempt won't be more productive, whilst successful search attempts won't deplete the tile's stock of resources. All tiles have a base "Search Chance" assigned to them and a table of different items that can be found there. These rates and tables are documented in the List of Locations.
The probability of finding something is modified by various factors, and all percentages are additive, not multiplicative: if a tile has a base search chance of 30% and a character receives a +10% bonus (for whatever reason) then the character would have a 40% chance of finding something.
For most characters, the best search rates can be gotten by searching during the Day in a Powered Building.
Day and Night
Searching during the day does not increase or decrease the chance of finding something. In Elysium the plane is always bathed in sunlight and thus considered permanently in daytime.
Searches during the night are conducted with a -10% penalty. Stygia is a plane of perpetual night and thus considered permanently in nighttime.
The influence of Classes on searching
Demons are familiar enough with the nature of Stygia to gain a +15% bonus to searches in that plane. This bonus stacks with the -10% penalty for searching in the eternal night for a net bonus of +5%. Revenants prefer the cool of the night to the harsh light of the sun, and thus gain a -10% penalty to searches during the Daytime (instead of Nighttime) and gain a +20% bonus during Nighttime (which imposes a -10% penalty) .
Searching inside a building whose lights are on (denoted by the lightbulb in the lower left corner of the tile icon) grants a +10% bonus to the search. There is no penalty for searching in a building whose lights are off (or simply don't have lights). The skill Engineering allows characters to influence the lighting in buildings when standing outside of one.
Skills and Status Effects
The Search skill gives a +10% bonus to searching.
The Opal Syndicate gives a bonus to searching with a magnitude depending on the character's standing within the guild.