We've got multiple ways, actually! While the city and most of the populace was wiped out, there's still a HUGE amount of archaeological remnants that we can study - those remnants give us an idea as to what the homes looked like and the layout of the ancient city. Punic architecture seems to have adapted a blend of cultures - as shown in this picture here. However, one of my absolute favourite things to show people when they ask about Carthage is a satellite picture of that exact image you posted - just a couple of millenia later. Here's the harbour today - it's rather distinct :)

Finally, we do have a rather wonderful - even if it's probably exaggerated - description of the city by Appian, which is available here. Hope that helps, and if you'd like to learn more about them, Dexter Hoyos' The Carthaginians is a godsend!