With regards to the Roman destruction of Carthage, the initial system of destruction for the city was fire. Once the siege was completed and Carthage had been breached, the Romans set the city alight and allowed it to burn for approximately ten days. This would have destroyed the majority of the non-stone buildings in the city and severely weakened the more solid Carthaginian structures.

Most buildings in the ancient world would not have been made of stone but of combustible materials such as wood or thatch. Even many stone structures would have had wooden roof beams or wooden roofs. This would also allow the fire to spread much more efficiently and severely weaken any structure that remained possibly leading them to collapse.

For any buildings that would remain standing after the blaze, the heat from the fire would weaken the stones in melting the mortar or connecting material. Once a few stones shifted it would put uneven strain on the rest of the structure which could lead it to collapse.

Once Carthage had been burned to the ground, the Romans entered the city and dismantled any structure which remained standing until, as Polybius describes in his Histories, 'no one stone stood upon another.' We do not have an exact timescale with regards to how long it took the Romans to dismantle the remains of the city, but given that it took ten days for the fire to subside and the estimated size of the city it can reasonably be assumed that it would have taken the Romans much longer to clear the site of any remaining structures.

It is plausible to infer that in cases where cities were razed, setting them on fire would be the logical choice. However, I hesitate to use the Roman destruction of Carthage as a standard example. The total destruction of the city of Carthage was extreme; there is a reason why the most famous razings in history are often described as the destruction of Carthage and the probably mythical story of the destruction of Troy. In the ruling elite of Rome at the time there was an intense feeling that in order to secure the political and cultural dominance of Rome Carthage not only had to be defeated but erased from existence. The purpose of the Third Punic War was exactly that, and the end goal in mind was always to raze the city to the ground in the most extreme way which would not have been the norm. There was a reason why, as Plutarch quotes, Cato the Elder would end every one of his speeches in the Senate with the words 'Carthage must be destroyed.'

To summarise, the standard method of the destruction of a city in the ancient world would be to set it ablaze. This was the most effective method of widespread destruction due to the vulnerability of most buildings and the compact nature of cities such as Carthage. The timescales would largely depend on the size of the city and the level of destruction the victors desired to apply.