More nearly serious answer: it depends on what you have in mind for the setting. A more realistic medieval army might mostly 'forage' (steal food from the folks they're conquering as they go, serious supply lines were, IIRC, a Napoleonic thing? (history buffs can correct me on those). A fantasy army might have fantastic foodstuffs like Tolkien's lembas or magic items that produce food and water (D&D has had a few of those over the editions - Decanter of Endless Water, Murlund's Spoon). An evil humanoid army might kill and eat their foes as they go. Spellcasters can create food. In a sufficiently fantatic world, where little things like the 2nd Law of Thermodynamics aren't even rumored, an army could use weird/impossible closed-loop provisioning strategies, like mounts that give birth every night, after which you butcher and eat them, sharing the food with their young who grow to full size by morning, and off you ride.
edit: specific D&D races? Well, in one edition, Dwarves made 'stonemeal biscuits' that were a day's worth of food in a compact package if you could bear to chew them. Elves, of course, would get the traditional tasty cakes from Tolkien. Gnomes might have magic mushrooms that grow instantly but only nourish gnomes (giving anyone else hallucinations). I could see an Eberron setting having canned goods and huge, intimidating-looking seige engines that are really just carrying the tons of canned goods it takes to feed an army. FR, IDK, I could imagine common infantry men griping about having to use Rings of Sustenance for weeks on end. More normal humans, I'm betting, would forage, because we're supposed to be all resourceful and adaptable.
Orcs would eat whichever of the above ran the slowest at mealtime.