After the Persian Wars Athens formed a defensive league against any future Persian invasion. This league was made up of Aegean islanders and the funds were kept on the island of Delos, therefore it has become known as the Delian League. Athens, as the strongest member and initiator of the League, oversaw the collection of funds and military organization of all the members. Eventually, Athens seized absolute control of the League and moved its treasury to Athens where the funds were used for the Athenians' exclusive benefit. Furthermore, any League members who withdrew or failed to dole out their share of funds or soldiers were harshly punished by the Athenian enforcers. Basically, Athens had used the excuse of the Delian League to create its own little empire to which Sparta, the previous claimant of supreme power in Greece, naturally felt threatened.
There are several examples that present the rising of tensions between the Athenians and Spartans. One of the first is when Athens set an example of what type of imperial enforcer they would be with their response to the island of Thasos' withdrawal from the Delian League. Thasos had control of a considerable gold mine on mainland Thrake, just north of the island, and Athens was demanding a lot from the island in its share to the League funds. Feeling exploited the Thasians revolted, to which the Athenians responded by besieging the island's capital city, destroying its defensive walls, seizing the Thasian naval fleet, and demanding payments, while also taking direct control of the mines in Thrake. Much like the Mafia, Athens made the statement with Thasos that there was no walking out on the gang/League. This action sent up warning signs to the Spartans about what exactly was Athens intending with this League when they treated its member with such harsh ascendancy.
The next scenario raising tensions was when the cities of Megara and Argos got into a dispute with Korinth over commercial shipping territory. These three cities were part of the Peloponnese and fell under a loose alliance with Sparta. So when Megara asked Athens for aid in the conflict and Athens provided it this action was not only an Athenian attack on a Peloponnesian city (Korinth, and also numerous other cities along the Korinthian gulf and Akhaea involved), but an appropriation of one of Sparta's allies (Megara).
By receiving the support of Athenians in their feud with Korinth the Megarians were forced to join the Delian League (i.e. Athens' empire) which included hosting an Athenian garrison at the Megarian port. After several years Megara got fed up and revolted, expelling the Athenian presence, thus realigning themselves with the Peloponnesians/Sparta. Meanwhile, in Euboea the cities of Khalkis and Hestiaea also revolted from the League and, like Thasos, suffered severely for it from the Athenians. This is when the Spartans first responded and sent an army as far as Eleusis, on the northwestern border of Athenian territory. However, due to smooth diplomacy, or maybe bribery, on the parts of Athenian general Perikles and Spartan King Pleistoanax the invasion was called off and a peace treaty arranged. This ended the First Peloponnesian War.
About a decade later in central Greece the two factions of Phokis and Amphiktyonic-Lokris were disputing who would hold authority over the oracular sanctuary at Delphi. Athens sided with the Phokians and Sparta the Lokrians. This, what is known as the Second Sacred War, remained a side dispute through much of the Peloponnesian War.
The Second Peloponnesian War (the real meat of the Peloponnesian War) started off about five years later when the, never truly eased, tensions reached a new breaking point over the Korinthian colonies of Epidamnus, in the extreme northwest(modern Albania). The Korkyraeans and Korinthians were conflicting over whose faction should have control of Epidamnus and when Athens sent ships, as a strictly "defensive" aid for the Korkyraeans, it strongly tested the terms of the treaty previously made by Perikles and Pleistoanax. Plus, Athens had recently placed a trade embargo on Megara. Athens was again imposing itself on Peloponnesians.
Meanwhile, at Potidaea in far northeast of Greece, the city was planning a revolt from the Delian League, (having previously been made a subject). As the mother-city of the colony Korinth sent Potidaea support in what would be a several year long defense against the Athenians' siege. At this point the conflicts between Korinth and Athens, along with several other Peloponnesian cities like Megara, forced Sparta (Korinth's closest ally and leader of the so-called Peloponnesian League) to reconsider its peace with Athens. In 431 BC the Spartan King Arkhidamus II marched an army against Athens, and the War was on.