Villa staged the Columbus attack out of desperation. The Carranzistas had decively smashed his army at the Battle of Celya in April 1915. As his forces melted awy and the federal forces relentlessly closed in Villa in desperation perpetrated the Columbus raid and an earlier atrocity when his forces executed a party of American mining engineers and technicians brought to Mexico by the federalistas to try and restart the vital copper mining industry. The purpose of both of these actions, beyond blind revenge on Americans who Villa blamed for his defeats was to try to embroil the US in a war with Mexico. If war came, Villa reasoned, he would become a de facto ally of the Carranza government and as such would be able to rebuild his power base in Chihuahua.
It didn't work out that way. While US forces came near to sparking a war as the Carranza government attempted to hamper and block movement of US forces in Mexico and two armed clashes resulted the Wilson administration carefully steered a course that kept US forces in Mexico hunting Villa without succumbing to strong domestic pressure for a general attack on all Mexican forces in the area of operation.
Whether through deliberate Carranzista leaks of information or through intel sources that were never disclosed, Pershing's forces had good enough intel about the Villistas that significant pieces of his dwindling forces were destroyed or dispersed in several engagements. Villa himself had the humiliating experience of being reduced to moving like a fugitive about what had been his personal stamping grounds and on on occasion was forced to hide is a cave for a day as US forces scoured the area he was in.
Villa never recovered from Celaya and he didn't get his war to jump-start his fortunes. The Wilson administration, frequently, and justifiably taken to task for making policy based on wishful thinking in the Punitive Expedition demonstrated a sophisticated grasp of political realities. The goal was to punish Villa and his bandit army not a war with Mexico to distract the US as a confrontation with Germany was looming.
The following site has a very detailed look at the Battle of Celaya and its victor Alfredo Obregon, who was if anyone could be described as such the greatest figure to come out of the Mexican Civil War:
http://europeanhistory.about.com/library/prm/blbloodandsilverprm1.htm
The best book on the US Army and the Punitive Expedition is 'Blood on the Border' by the late Clarence Clendenning.