Map of normans in Southern Italy

An Overview
More detailed account here

Beginning of the 11th Century- The Norman Conquest of southern Italy begins.
The first adventurers from the coast of Normandy, France, hire themselves out to the rival rulers of Benevento, Salerno, Naples, and Capua. As a reward they are given the city of Aversa. But as their numbers increase, the Normans band together to fight on their own.

AD1053-1059 -By this time Robert Guiscard (i.e. "the Wise", or, "Wily") has established a Norman kingdom in southern Italy. He conquers Calabria (the toe of the Italian peninsula), Benevento (1054 A.D.), and allies himself with Pope Nicholas II (r. 1059-1061), whom he protects from being dominated by Germanic rulers, and receives papal sanction to rule Calabria, Puglia (the heel of the Italian peninsula), and the island of Sicily. Robert sends his younger brother Roger to conquer Sicily, and himself sets out to conquer Puglia from the Byzantines.

AD1071 -Robert Guiscard captures Bari. With Puglia conquered, and with it Byzantium's rule in southern Italy ended, Robert next sets out to conquer Constantinople. But he is called back by Pope Gregory VII (r. 1073-1085) to defend the papacy against the Holy Roman Emperor Henry IV.

AD1084-Robert Guiscard captures the city of Rome from Henry IV's army. But when the people of Rome revolt against Robert's army, Robert sacks and burns the city.

AD1085-With the death of his brother Robert Guiscard, Roger becomes the ruler of Norman Italy or the "Two Sicilies" as it is called -- i.e. of the island of Sicily and the southern half of the Italian peninsula.

AD1091 - Roger Guiscard's conquest of the island of Sicily from the Saracens. The Moslems of Sicily and southern Italy are Berbers from North Africa (the race of St. Augustine) and Spanish Moslems, a diverse people but they are all called Saracens ("People from the East") by the Italians.

AD1101-1154 -During the reign of Roger II, a nephew of Robert Guiscard, Naples and Capua are added to the Norman Kingdom. Abruzzo is captured from the Holy Roman Emperors, and North Africa from Tripoli to Tunis is taken from the Saracens.

AD1130- Roger II changes his title from Count to King. The capital city of his "Kingdom of the Two Sicilies" is Palermo.

AD1194- Roger II's heirs, who have already lost the Norman's North African possessions, end Norman rule in southern Italy by surrendering the Kingdom of the Two Sicilies to the Holy Roman (i.e. German) Emperor Henry VI under the pretext that Henry had married a woman from the Norman court.