It varies quite a lot by time and place, especially regarding the nature of the organization raising the army. Greek city states' armies were naturally smaller than the Romans' continent straddling empire, and there was plenty of room in between. Nevertheless, some broad conditions apply that limited the size of even the largest (field) armies.

Until the Industrial Revolution, if you wanted to move something, you either needed muscle or sails. In terms of military application, armies were limited by what soldiers could carry, and what mules, oxen, and horses could pull, which was in turn limited by the road network available.

In the 19th century, the Prussian General Staff carried out studies, and found that the largest force you could supply along one road entirely with horse pulled wagons was about thirty thousand men, typically organized into an army corps (then the smallest unit that would have infantry, cavalry, and artillery of its own). Furthermore, the furthest an ox can pull a cart loaded with grain is about 150-180 km without refilling; at that point, it will have eaten everything in that cart, and there would be nothing left to deliver.

Geoffrey Parker explains the supply conditions of 30,000 men in 16th century Europe. The expected daily ration for a soldier was 1.5 lbs of bread and 1 lb of meat/cheese/fish, and six pints of beer. Just for the daily bread, the army would need twenty tons of flour; a week's supply of flour, with ovens and firewood, would take up 250 wagons. Providing 1 lb of meat a day would require the army to slaughter 1500 sheep every day, and that's not including supplies of ammunition, clothes, equipment, fodder, and so on.

A supply route could be stretched further if the troops confiscated supplies from civilians along the way, or carried a greater portion of the supplies on their backs, but there's a point of diminishing returns on this; 30,000 men on the road is about a day's march long, so if something happens at the front of the column, it'll take all day for the guys at the rear to make it to the action. When in friendly territory, an army can also shore up its supply situation by establishing chains of supply depots, where supplies can be stockpiled when not urgently needed; this is how the Spanish were able to repeatedly move tens of thousands of men from Spain to the Netherlands through Italy, France, and Germany in the 16th and 17th century.

The idea then was to maximize the number of men in battle by dividing up into columns that were close enough to support each other in case of battle, but were far enough away to keep themselves supplied, either by not having to share roads or pillage from the countryside.

There are limits to how applicable these guidelines are to ancient armies, but they provide good context for evaluating the army sizes reported in ancient textual sources. For example, when Herodotus or Arian describes the Persians invading with millions of soldiers, that's completely impossible, because only so many men can fit on a road, there's only so much grain available in the countryside, you can only move so many wagons full of food and water along a road on any day, etc.

For actual examples of ancient army sizes, the Punic Wars are a good case study. By this time, the Roman army structure was well established. Rome had two consuls; each commanded an army. Each army consisted of two Roman levies of 4-5,000 men each, as well as two wings (Alae -> ally), also of about 5,000 men, for about 20,000 men per army per consul. Sometimes, both consuls would march together, commanding the combined armies on alternating days, bringing the total to 40,000 men in the Consular armies, though legions would be raised outside this structure as well. It's important to keep in mind, though, that the Second World War was one of very few wars in human history where battle deaths exceeded deaths by disease. When marching tens of thousands of men close together in unsanitary conditions, with widely varying immunological profiles through territory whose germs they have no exposure too, a significant fraction of the force is going to be diseased.

With this in mind, we can probably accept as accurate the army sizes reported in ancient sources for the Punic Wars, especially since skirmishes between foraging parties became central to Roman strategy. For example, at the Battle of the Trebia, Hannibal's army fought with 30,000 men, and Sempronius with about 40,000, both within the general limitations of pre industrial logistics. By this time, the Roman military confederacy controlled most of Italy, and Hannibal's family were practically sovereign rulers over much of Spain, and encountered many Gallic tribes hostile to Rome on the march over the Alps and through northern Italy; both sides had large manpower pools to draw on. Later in the war, the Romans raised the largest army in their history; four legions and four Alae per consul, marching together, adding up to nearly 90,000 men. I think this is about the limit of what an ancient army can do.

This is much larger than hoplite era warfare between Greek city states; the largest battle of the whole period, Mantinea, saw fewer than ten thousand men fighting for the opposing leagues of city-states. These soldiers were largely amateurs, levies which fought simply and without much detailed organization. When Alexander the Great led his expedition into Asia, he had just under 40,000 men at the Battle of Granicus; about half of this army came from his kingdom and were professional soldiers, and the other half were allies from all the Greek city states and mercenaries.

TL;DR It varies a lot, from a few thousand in the case of Greek city states, capping out at about a hundred thousand as an absolute ceiling, with 20-50,000 being large, but by no means unprecedented, from the time of the 4th Century BC.

Check out

The Military Revolution and The Army of Flanders and the Spanish Road by Geoffrey Parker for details on premodern logistics

The Campaigns of Napoleon by David Chandler has a section describing Napoleon's art of war, and goes into detail regarding the division of the army into corps on the march.

http://www.legioxxirapax.com/zasoby/The_Logistics_of_the_Roman_Army_at_War_(264BC_-_235AD).pdf

this book gives a good look at the logistics of the Roman army specifically.