If an ordinary adventurer wants to hide, they must make that decision before a surprise roll is made. For example, if they know that a guard will be walking down a corridor at some point, they can hide around a corner. There must be some kind of cover. There's no "hide skill", but the cover used may give +1 (partial cover) or +2 (full cover) to the surprise roll. Similarly, if an adventurer takes steps to reduce noise, they can move quietly, getting +1 to surprise, or +2 for extreme measures. These modifiers do not stack.
(I use "surprise on 5+ on 1d6", which makes adding bonuses directly to the roll easy. If using the more standard "surprise on 1-2 on 1d6" mechanic, add the bonus to the target, making it "surprise on 1-3" or "surprise on 1-4".)
Cleverness may matter. If it seems reasonable that the adventurer may leave subtle clues to their presence, even when not visible or trying to be quiet, the adventurer only gets the bonus if either their Int or Wis is higher than the target's Int or Wis.
Speed may matter. If there's a chance that the adventurer could notice the opponent first, they can dart for cover if their Move is higher than the opponent's Int or Wis, whichever is better. This only works if the adventurer is not surprised, of course.
A thief does not need cover, only shadow, nor do thieves need special equipment to reduce noise, other than avoiding metal armor. The thief adds half their level (round up) to surprise when hiding in shadows or moving silently, plus any bonus for cover or sound dampening, if they chose to do so. If the thief decides to hide in shadows on the spur of the moment, they only need to dart for shadow, not for full cover, and they can do so if either their Dex or their level is higher than the opponent's Int or Wis.