As far as my limited knowledge of Roman history goes. During the early years of the Republic when Rome pushed outwards into Latium etc. they would turn conquered peoples into "half-citizens". Meaning they were not true citizens of Rome but prospered from alliance with Rome. In turn they were taxed and required to serve in the Roman Army. As far as I know this is how they sustained their forces in the early years.

Edit: they had also by the time of the second Punic War perfected the Citizen Army prototype. At any one time a citizen could be called up and so during a battle such as Lake Trasimene, not all the Roman Army would be fighting. But by the next conflict they would have called up more citizens.