The Spartans main strategy was to use their might and the amount of soldiers they have on land.
The Athenian strategy was to exhaust the enmies and use their large naval fleet
The war was declared in 431 BC.
The Spartans would burn all of the food supplies after marching into Athens territory and other things. Later in the war in 415 BC they would send a 20,000 men naval fleet to one of athens allies and hold attacks for 9 years.
In 421 BC Athens and Sparta would sign a truce after getting tired of the war.
In the end Athens got their military beaten and their city was in political turmoil. And Sparta became the biggest city state in Greece.