Or more directly, how was supply dealt with if a force in Milan wanted to wage war on the Papal States, thus having to pass through other republics or duchies? Was sea travel common? Or did the forces just coalesce near a battlefield?
E: I am essentially asking about the logistics involved in warring with a state or entity not directly bordered with your own.
When Pope Innocent IV paid the ransom to the condottieri of the Great Company to lift the siege of his papal city Avignon in 1361, he set precedent for the activities of mercenary armies that rampaged across Italy for 200 years to come.
The papacy had sought to avert a crisis in Provence, the cities of which were threatened by the armies of the Great Company, an amalgamation of disaffected soldiers and horsemen from the 100 years war. So, after months of useless threats and excommunication, Innocent IV paid the Great Company to leave (reportedly 100,000 florins), and as part of the arrangement he negotiated for the mercenary army to move into the service of the Marquis Montferrato, lord of Turin and imperial vicar of Piedmont, to fight their common enemy the Viscount of Milan.
While Innocent IV managed to remove the threat from Avignon and the surrounding cities of Provence, he encouraged the very model of warfare he despised. Some of the mercenaries dispersed to other parts of Europe. However the core of the Great Company, several thousand in number, moved on to the Marquis Montferrato. Although the papacy had avoided the crisis in towns in the orbit of Avignon, this same Great Company razed and burned its way east across Marseille, Nice and the towns of Piedmont enroute to Turin.
The Great Company produced the remarkable figure of John Hawkwood, the English knight who would soon become leader of perhaps the most infamous condottieri, the White Company, composed of Germans, Swiss, English, French, Spanish.
The White Company's activities in the north and middle of Italy reflect the typical picture of mercenaries of this age. This was a geographically small, dense area of Europe which could be traversed by horseback and tent very fast. The money and other ransoms earned by the companies managed the flow of provisions, even in winter (winter combat was incomprehensible to the first generations of these besieged Italian cities). Logistics was nothing more than sieging and sacking villages along the way, extorting repeatedly from the same cities over and over by playing cities like Florence and Pisa against one another.
For the condottieri, borders meant nothing but opportunities for more income; the fields that lay there nothing but a place to camp.
Reading:
William Caferro, John Hawkwood: An English Mercenary in Fourteenth-Century Italy (JHU, 2001)
For those with little background in late medieval history and want popular history at a large scale along the lines of Tuchman's A Distant Mirror: The Calamitous 14th Century, Frances Stonor Saunder's The Devil's Broker: Seeking Gold, God and Glory in Fourteenth Century Italy (HarperCollins, 2005) is a reasonable introduction to the condottieri.
I would like to expand this question and ask for some book source about Condottieri.
Hawkwood: Diabolical Englishman by Frances Stonor Saunders is an excellent book about one condottiere in particular and the phenomenon in general