This is a rather broad question to answer, as artillery during the Second World War was rather varied between nation and changed throughout the war, as well as having an incredible number of different governing conditions. However, if we assume we're talking purely about British artillery, the rough time taken for an artillery unit, with no pre-preparation, to range and fire on a given target, was expected to be 8 minutes during the Desert War. However, fire on a target that had not be pre-ranged or otherwise planned for was increasingly less common as the campaign went on, resulting in shorter response times, as gunners already had areas registered in case of calls for support, or were kept under centralised command in an Army Group Royal Artillery, which could result in very short response times (1 or 2 minutes), or massive concentrations of fire. In Normandy for instance, 'the British were skilled in concentrating fire very quickly, say within 5-10 minutes, from hundreds of guns irrespective of unit boundaries', a skill very useful considering the German predisposition to counter-attack throughout the war.

Dependent on which nations and units you are particularly interested in I would suggest reading more specifically around the topic, and on the British in particular I would recommend Stig Moberg's Gunfire, which covers methods, equipment and evolution throughout the war.