First, they imported a LOT of food from other parts of the empire. Rome is now built on the remains of Roman food packaging material: broken up pottery. Romans mainly lived on what is know as the mediterranean triangle: Wheat, wine and olive oil. Bread made up 70 to 80% of most of the Romans diet. Three kinds of food that are pretty easy to transport over longer distances. There were huge imports of grain from north Africa and Egypt. Rome lived on that grain. Wine and olive oil came from almost everywhere.

But that wasn't all. Not many people know this, but Rome imported many fresh fruits and vegetables as well. There are many amphorae found that had stones of fruits in it. Also huge amounts of animals were herded to the city every year, especially from the lower half of the Italian peninsula.

And now the second part. Romans were amazingly good at growing food. The efficiency of agricultural land and labour that the Romans had at the end of the republican era was only surpassed in the 19th century western Europe.

The level of agronomic knowledge was quite high. There are a few Roman agronomic handbooks left and they are very good. Romans discovered 'new' plants in the east and spread them all over their empire. Roman farmers actively cultivated bigger and tastier vegetables. In horticulture especially they were very good at managing the humidity of the soil by digging canals, using rural aquaducts or burying layers of potteryshards to facilitate drainage. Also the variety of different cultivars of plants within the species was so large that Romans had the luxury of choosing which cultivar was suited best to the climate and soil.

Also the Romans had excellent systems of crop rotation: alternating two or three crops of cereals one of legumes and one with fallow or green manuring (the mixture of plants sowed for green manuring being chosen for the type of soil, the crops of the cycles before and the usefullness as animal fodder).

Romans also had a lot of lifestock. Roman cattle were twice as heavy as those in the periods before and after the Roman golden age. Most Roman farmers had some livestock kept stabled for use as source of power, milk, meat and leather but most importantly, for poop. Without poop there is no civilization and the Romans knew it (so much even that it was forbidden by law to sell a farm and its manure heap apart from each other). When land is so intensively farmed as it was around Rome. You think everybody living in Rome was just shitting in the Tiber? Nope, poop is worth money. That shit was carted out of the city to fertilize arable land for miles upon miles around Rome.

• Mattingly, D., ‘Oil for export?’ A comparison of Libyan, Spanish and Tunisian olive oil production in the Roman empire’ Journal of Roman archaeology 1 (1988) 33-56.
• Kron, Geoffrey, ‘Archeological reports and notes – Roman ley-farming’, Journal of Roman archeology 13 (2000) 277-287.
• White, K. D., Roman Farming (Londen 1970).
• Frayn, Joan M., Subsistence farming in Roman Italy (Fontwell 1979).
• Morley, Neville, Metropolis and hinterland. The city of Rome and the Italian economy 200 B.C.-A.D. 200 (Cambridge 1996).

[edit] Put in some numbers.

Also, I would think that disease would be a major problem in those times with such a large population. Was the Roman public health system of aqueducts and sewers really that effective at preventing disease, or were epidemics common in ancient Rome?

A bit of a followup- how large was "Rome" at that time? What was the population density like? How tall were the houses? I ask because it seems like a million people is an awful lot for a city that doesn't have mass transit, elevators, etc.

A lot of the Roman's received annonae, a welfare payment of grain each month. To keep Rome fed, ships dropped off goods to the port city of Ostia which was downriver of Rome by the Tiber. Barges then carried grain from Ostia, up the Tiber to Rome.