We're usually taught about Hannibal's crossing of the Alps and a few major tactically genius battles against the Romans, climaxing with Cannae, but, afterwards, we tend to only remember the battle of his defeat, Zama. That's more than a decade of an enemy army in the homeland. How did he survive so long there, what did he and his army do? I understand that his plan was to convince Rome's allies to leave them and assist him, but how was that meant to be achieved during the time after Cannae?
The problem Hannibal had was that he didn't have a very good way to win the war. First, Hannibal felt he couldn't lay siege to Rome right after Cannae. His plan was to wreak havoc in the countryside, convince the nearby cities to defect to him, and choke out Rome to the point of suing for peace. Hannibal partially succeeded, but the Carthaginians never gained enough support to control Italy completely, nor were they blocked to the point of being wiped out until the other theatres lost.
First, Hannibal wanted to disrupt the Latium league, which would have cut off Rome from their nearby allies. However, few cities defected, and there never was a defection en masse. The largest defection was the city of Capua, which Hannibal meant to be the "capital" of his territory in Southern Italy. Even in this area around Capua, not all of the citizens defected. The Carthaginians were seen as foreign aliens, as they didn't share the same Greco-Roman heritage (the Carthaginians were Phoenician). This is a very important point, because Hannibal was relying on support form the local populations to actually defeat Rome. Without strong support of the local population, Hannibal couldn't gain very much manpower from the local population. As Rome had no intention of surrendering even when under threat, Hannibal couldn't break Rome.
Second, Hannibal didn't have reinforcements coming to help him in Italy. Hannibal never controlled a port in Italy until Tarentum was captured, and it was too late by then- Capua would fall shortly after. In addition, Carthage lost control of Sicily and was taking heavy damage in Spain, so there weren't many reinforcements to send. The only way for reinforcements to reach Hannibal was across the Alps like he had gone, and his brother made an attempt, but it wasn't enough to make a decisive difference; these forces under Hasdrubal were decisively defeated at the battle of Metaurus river. Hannibal's only option was then to take recruits from the local Italians, and this was not enough to greatly increase his numbers.
So at this point, Hannibal was at a stalemate. He had just enough recruits to replenish his forces, but not enough to increase his strength. He could capture and hold a city, but not all of South Italy. So as for what he actually was doing?
After Cannae, Rome mustered up a massive army by lowering the requirements to join. This, along with more competent leadership, allowed them to hold Hannibal at bay without major battles. Meanwhile, as Rome was decisively winning in Sicily and Spain, they just had to prevent Hannibal from gaining a strong foothold. Most of this decade was "armies marched and counter-marched across much of Southern Italy, frequently passing again over the same areas, both sides struggling to control the important cities and towns" (Goldsworthy 222). Rome couldn't fully defeat Hannibal, but they didn't have to: time would do it for them. While Hannibal controlled portions of Southern Italy, he couldn't control everything, and that made the difference between victory and defeat.
Sources:
Adrian Goldsworthy's The Punic Wars
Serge Lancel's Carthage: A History