We know the Roman side
How did the war start?
By 274 BC, the Romans had taken over all of Italy. Then a Greek city that was NOT in Italy asked the Romans to help it out in a war. This city was in Sicily, a big island near Italy in the Mediterranean Sea.
How did Carthage get involved?
Sicily at this time was divided in two parts. One half had Greek cities in it. The other half had Carthaginian cities. When the Carthaginians heard that the Romans were coming, they were afraid the Romans would try to conquer them, too. So they attacked the Romans.
At first the Carthaginians were beating the Romans, because to go to Sicily you had to go in boats, and the Romans weren’t very good sailors.
The Romans learned how to sail
But the Romans learned how to sail by capturing a Carthaginian (Punic) ship and copying it. And in the end they beat the Carthaginians and won the first Punic war. Now the Romans took over the whole island of Sicily, and made all the cities pay taxes to Rome and have a Roman governor.
The Romans had not conquered the city of Carthage itself, which was in Africa. But the Romans made the people of Carthage pay the Romans a huge amount of money, to pay for the war. And the Romans took control of the silver and gold mines on the island of Sardinia.
The Ancient Roman World, by Ronald Mellor (2004). Straight political history, For teens.
Classical Rome, by John Clare (1993). Easy reading. The whole political history from beginning to end.
The Romans: From Village to Empire, by Mary Boatwright, Daniel Gargola, and Richard Talbert (2004). Okay, it’s a little dry, but it is up to date and has all the facts you could want.
The First Punic War: A Military History, by J. F. Lazenby (1996). The only academic narrative account of the war in English.