I think I can answer some of this.

In the first decades of the first century BC piracy was a major problem. Indirectly the Romans themselves were at fault in this. Rome had destroyed Macedonia, crippled the Seleucid Empire, and helped the decline of Ptolemaic Egypt. All of these nations had maintained powerful navies, but with their decay piracy flourished and became an endemic in the Mediterranean. Mithridates of Pontus also encouraged this seeing them as useful allies against Rome. The coastline of Cilicia in Asia Minor was home to many pirate strongholds and there had been little headway in controlling the problem. The pirates were extremely numerous, sometimes operating in large squadrons and even launching raids on communities along the cost on Italy itself. Although the pirates did not have a single leader there were several chieftans and there seems to have been a degree of mutual co-operation between the various "Pirate factions". To explain the amount of problems the pirates could cause I can mention that they managed to raid Ostia and on a different occasion managed to kidnap two Roman Praetors.

Why was Pompey granted command of this? Even though Pompey was an extraordinarily good commander, his perfomances in the senate was lackluster. The year was 67 BC and it was clear he was missing the admiration his earlier victories (The Slave war for example) had brought him, and he began to make manouvers for a new command. The spectacular nature of his career so far in life ensured that this could not be a simple province handed to him at the start of next year. And a tribune called Aulus Gabinius proposed a bill creating an extraordinary command to solve the piracy problem once and for all. Piracy had gotten even worse in recent years and now it was threatening the vital grain supply that kept Rome fed. The details of the bill were very radical, granting Pompey vast numbers of troops and ships, and imperium (e.g. dictates the area/province(s) one had control over) that stretched over most of the Mediterranean, making him more powerful that most of the governors in the relevant provinces. While the bill makes no specific mention of Pompey it was pretty clear to everyone that it was intended for him and that he was the obvious and really only choice. The bill met much opposition in the Senate who argued that it was a mistake to grant that much power to a single individual in the Republic. The Senate being composed of individuals who cared for nothing but their own rise to power would much rather see this (and other) problems continue rather than seeing a man rise above them, and getting the credit for solving the problem.

The bill was promptly passed and Pompey set his organisational genius to solving the problem. He divided the Mediterranean into sectors and went through them one by one. Using the vast resources and manpower he had available the seas to the west of Italy was swept clean in a matter of only weeks. One of the reasons for this quick success was his willingness to accept the surrender of the pirates and their families and then settling them on good farmland in new communities were they could support themselves without resulting to piracy and violance. The pirates in the eastern half took only slightly longer to deal with and was handled in the same way. Pompey was once again the hero of the Republic and adored the admiration he recieved.

The conflict started and ended in 67 BC and lasted no more than a couple of months at the most. I don't think there's any book specificaly written on this subject. I think you'd be better off reading a biography of Pompey (or Caesar which I used as a source for this). The book that I'm citing a source below has a few sections dedicated to the piracy problem in the Mediterranean around this time.

Source: Caesar Adrian Goldsworthy