Copied from SparGamez...
My general strategy for Carthage is to take Sicily and fortify the island from initial roman countermeasures. I start by building defense in Spain and making sure the Celts won't MA with Rome against me. I go for the Ivory outside Leptis Magna as quick as I can for Ivory to upgrade Spears to Numidians. At this point I amass three seperate forces

. All this time I will build settlers to grab the dyes of northern Libya, and several other cities in a southwest direction from Carthago.
One attack force in Spain from the cities around Tingis and from Spain itself. One from the rest of Carthage that meets in Carthago to head to the northernmost Sicily city, and the last one in Leptis Magna (or my easternmost city) to go for a battle against Egypt.
Egypt is really easy to kill. a fair amount of War Elephants can lay waste to them. Rome is a lot tougher. I start working the Spanish force north, killing any Romans that have settled in Spain. At this point I usually MA with the Celts and/or Goths against Rome (if only to distract them) and I get the attack force in Sicily (includes Hannibal's army) to head to Calabria and take the city there (Croton, I believe) and I slowly will work north up to Rome.
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There are a lot of different ways to tackle this scenario, and I've personally been thinking a strategy of mostly ignoring Rome (unless it begins to runaway) and going straight to Egypt, killing them and then moving on through Persia or maybe a sea invasion of Macedonia.
In response to the settling projects of Africa, this is a good idea to spred settlers throughout all the habital non-Sahara parts of the continent, but to reach the domination limit we need 50% world population and 20% territory. Territory isn't that hard to get to, but it's the pop limit that is troubleesome, because a swarm of tiny sahara cities will contribute less population than that of a size 12 city.