How to Search for Quiescent Time in Chess

Chess is often played with a time limit so in a common chess game you might have a time control that something like each player gets two hours and then depending on how many moves are played there might be an additional hour to add. The computer is real constraints about how much time it has to search and how does it make the decision about how far into the future do we go? There are different strategies but sometimes when a position is really difficult we might want to spend more time on it and actually look further into the future.