Were rations shipped to campaigning armies, was food taken from hostile towns/cities and encampments of defeated enemy armies? If it was a combination of the above, what proportion (approximately) of food came from respective means? To avoid uncertainty, let's say this is concerning late Republican or early imperial Rome, though Alexander's campaigns or Persia under Cyrus would also be appreciated.
I know a little about provisioning navies during the Peloponnesian war: Triremes did not usually carry supplies. They had to land near cities that supplied a market. The sailors would buy food and prepare meals on the ground. This is how Lysander won at Aegospotami - the Athenians established their base miles away from the nearest market. One day they all wander off to buy lunch and Lysander (who had spies watching) captured the abandoned fleet.
One exception to this was the voyage the Athenian sacred trireme Salaminia made to Mytilene to revoke the decree of executing the population in 427 BCE. The Mytilenian ambassadors at Athens provided food for the crew, and they rowed non-stop in shifts to reach the city before the Athenian army there executed the order. It is the fastest trireme voyage on record, and rowing in shifts allowed part of the crew to rest and eat while at sea.
All of this is derived from Thucydides and Xenophon. I can probably find specific references later if you like.
For a convergent viewpoint, we can look at the way Aztec armies were supplied on the march. Accompanying the soliders would be large number of professional porters (tlamemeque) who would carry the necessary provisions for both themselves and for the soldier they were supporting. Porters were not necessarily permanently affixed to the marching army, but could be "loaned" from tributary cities along the route. An army marching directly from Tenochtitlan, for instance, might have pre-planned stops along it route to refresh both porters and supplies.
Hassig, in Aztec Warfare makes much of this limitation, noting that the lack of pack animals necessitated the use of human porters, which consumed the same food as the soldiers, which necessarily limited the range and timetable of Mesoamerican armies (I discuss this a bit in an old comment on Aztec sieges). Hassig specifically calculates that there would need to be 1 porter for every 2 warrior, based on a diet of 3600kcal/day and an average carry weight of 23kg/porter, with a max travel time of 8 days without resupply.
We unfortunately do not have the kind of records to say whether Hassig's model is accurate or not, but we can see the practical effects of logistics in the expansion of the Aztecs. Initial efforts would establish tributary/friendly polities, which could then be used for more expansive campaigns later. If we look at the their incursion into what is now Oaxaca, for instance, we can see how this worked. End of reign incursions by Ahuizotl were followed up by his successor, Motecuhzoma Xocoyotl, following the same general route into the are, using the previously conquered areas as launching pads for even greater subjugation of the region.