The war is so complex that it has 4 stages, with the belligerents changing sides back and forth. Venice, for example, changed sides from fighting France and the Papal States in the beginning, to fighting the Papal States with France in the end.
The 1st Italian War resulted in a very fragmented Italy, which the Borgias tried to take over many regions, especially Romagna. The lords in Romagna, wanting to avoid losing their estates, pleaded to the Venetian Republic to become part of the Republic in exchange for their estates protection. Venice agreed, and annexed the provinces in question. The Papal States, discouraged that there was a very powerful Italian state that could counter their power, encouraged the Holy Roman Emperor, Maximilian I, to attack Venice. This Imperial venture failed, so the Papal States, with the League of Cambrai (France, HRE, Spain, Ferrara, & PP) attacked Venice over a slight provocation, namely that Venice had named a religious official without the Papal States' approval or advice. This was just an excuse, however, to launch a destructive war to curb the Venetian Republic's power.
The Papal States, now realizing that having a strong French presence in Milan and N. Italy was much more dangerous, joined the Venetians, who were already fighting the French (because of the Papal States) and the two Italian powers began campaigning against France.
The war was going badly for the Papal States and Venice against France, so the Pope used his power again to form a "Holy League", consisting of Venice, Spain, the Holy Roman Empire, and surprisingly, England, who wanted to take down their enemy.
The best part of the saga, the fourth stage consists of Venice being betrayed by the Papal States because it was not included in the peace negotiations, so it takes revenge by joining France against the Papal States, and the "Holy League" is defeated. Venice and France decided to split North Italy between themselves.
The lesson to take away from this is, back in the 1500s, alliances were as good as pinky promises. Venice, however, went from the verge of destruction, facing hundreds of thousands of French/Austrian/Spanish troops to ultimately winning the war, the big picture, using very intelligent diplomacy and a dodge-all-major-conflicts war strategy that Pitigliano and his Venetian Army used, led miraculously to status quo in territories from 1508 for Venice at the end of the war. The war ended with France retaining Milan and Venice retaining its lands more or less the same as 1508.