The very earliest foreign mercenaries in Italy were veterans of nearby conflicts; typically veterans of wars in France and/or Germany. Indeed, the first wholly foreign company in Italy was hired in the early 14th century by the Marquis of Monferrat, unsurprisingly the ruler of a polity in Northwestern Italy, near France.

The details of the conflict between the Monferrat and its neighbors aren't really important (suffice it to say that the Monferrat was threatened on the west by the Counts of Savoy and to the east by the ruthless Visconti of Milan). But what is interesting, and altogether clear, is that a lull in fighting during the Hundred Years War had resulted in bands of armed men dispersing all over the France; it wouldn't be long before they would discover, through one channel or other, that they could find ready employment just across the Alps in Italy. French authorities, especially local ones, tended to encourage and sometimes even facilitate the transition of men-at-arms to new employment. Indeed the presence of bands of armed men, far from home and with no reason to exhibit restraint, would continue to be an issue for the duration of the long conflict between the English and French monarchies. These individual bands, while numerous, were seldom large and for this reason difficult to stamp out. Just as an example, Arnaud de Cervole was a particularly charismatic knight and petty lord formerly the service of the French monarchy who never personally commanded more than a hundred men. However when there was loot to be had unemployed veterans could gather rapidly, and while pillaging after the Peace of Brétigny Arnaud de Cervole was able to round up some two or three thousand men at arms and hold the imposing fortress of Avignon to ransom!

French ecclesiastic authorities, together with the french-based Papacy, were instrumental in negotiating with Arnaud's men and finding them new employment; but in all probability most would have probably found their way to Italy regardless. Military recruitment by Italian authorities wasn't all that much different than recruitment in France, meaning commanders fundamentally enlisted whomever was willing to fight regardless of origin and identity (all the better if they were already well trained and battle-tested). Indeed, mounted men-at-arms were often military adventurers: typically men who had been born into minor landowning families but perhaps stood to inherit little more than a somewhat recognizable surname, prowess with arms, and a horse. These men were quick to attach themselves to powerful figures of authority, offering their service in battle in exchange for lodgings and a place in their retinue.

So while Arnaud de Cervole was hired by King John II of France to hunt down other brigands, other leaders in his band instead accepted employment with the aforementioned Marquis of Monserrat, notably a German named Alberto Sterz, and the Englishman John Hawkwood. The names of some of the knights which followed them (at least the ones that have been passed down to us) reveal a wide array of backgrounds, Burgundy, Piedmont, Savoy, Provence, more generally Occitania, maybe Basque Country or Catalonia, and of course England: Bernardo della Sala, Robert Briquet, Esprit, John Creswell, Naudon de Bageran, Lamit, Bataillé, Esparre. I don't know if the decision-makers in the Monserrat would have been fluent in the French spoken at the time; although the Savoyard aristocracy across the border would certainly have been. In any case, Old Occitan isn't all that different from the Gallo-Italic dialects in Northwestern Italy, and for the cosmopolitan mercenaries language barriers seem to have been easily overcome.

But although the presence of foreign mercenaries certainly draws the most attention, Italians were by far the most common signatories of the "Condotta Militare," that is to say the military service contracts which emerged in Italy over the course of the fourteenth century. Some Italian states, notably the Republic of Venice, flanked their condottieri with designated political-military appointees who would oversee supply and organization, but most states allowed their condottieri a free hand in nearly everything: recruiting men, supplying their companies out of the provided budget, and appointing officers to help them. Presumably, then, a condottiero would make sure that an officer overseeing foreign recruits would know both the language spoken by his men and at least some Italian; but while there certainly were German, French, and English condottieri and sub-condottieri recruiting a broad spectrum of nationalities in their companies, by and large most Italian states hired Italian captains who raised primarily Italian regiments. In fact, many Italian rulers employed condottieri from amongst the attendees at their own court! But of course there's certainly no rule set in stone; very few of the condotta contracts specified geographic limitations on recruitment (as far as I know, only the Venetians ever did this some several hundred years later, well into the Early Modern Era).

You can probably imagine by now that the companies around these condottieri would fluctuate widely in number. In times of peace, even the most famous and decorated captain might have only a few hundred men in their retinue. Some very successful condottieri were able to worm their way into being granted small semi-autonomous fiefs from which they could round up a stable number recruits and draw vital supplies and material, with the added bonus that the condottiero in question (and his recruitment network) was now permanently tied to an employer. But most unemployed condottieri would try to move swiftly from place to place, and suffered heavy desertions if they could devise no ransom or find no employment. There are also accounts of companies "dispersing" after a particularly resounding defeat. Only when a captain earned a new contract could recruitment could begin in earnest again and companies would again swell in numbers. But if the life of a professional soldier was unpredictable in times of peace, it could be even more unpredictable in times of war; so condottieri were often unwilling to commit to battle unless they were certain of the outcome, and increasingly warfare became a slow game of hypotheticals, subterfuge, positioning, and theatrics.

When two armies encountered each other, the confrontation was often short and could even be relatively bloodless. As soon as one side appeared to have advantage the "loser" would attempt to swiftly withdraw in good order (often to the frustration of their employers; "They avoid defeat just as long as they avoid battle" wrote Macchiavelli, who as a statesman in the Florentine government would undoubtably have been frustrated by countless contractors who made meticulous preparations for battle only to decide the odds were against them and withdraw). However, this hyper-cautious approach to battle didn't mean war was inconclusive, in fact when one side has a clear advantage it led to very swift victories; decisive sieges in particular were very common (especially via negotiated surrender). Between the 13th and 15th centuries, the Milanese, Paduans, Veronese and Florentines were almost continuously involved in some kind low-level warfare, bullying smaller surrounding towns into submitting and constructing networks of fortified burghs around their capital. Oftentimes, these sieges were perpetuated by the mercenaries themselves, who needed to be occupied lest they start pillaging; creating a vicious cycle by which larger, richer cities were constantly hounding out weaker ones, using war to both keep impressing their own idle veterans and guard against their enemies (doing the same thing).

Thank you very much !