After that Athens started making offensive moves, largely due to the politician Alkibiades. Many of them were disastrous, especially the Siciliy expedition: Alkibiades fell from grace and then betrayed Athens as he convinced the Spartans to intervene.
Alkibiades treachery wasn't limited to that, he fell out of favour of the Spartans and he defected to the Persians, to whom he proved a valuable advisor. The Persians supported the Spartans with money wich is why the Spartans won in the end, chiefly because it could afford them a huge navy.
You are being rather unfair to Alcibaides. Foremost, it was not him who first adopted the more agressive policy. After the death of Pericles, Cleon and Nicias would come out as the top political leaders, with neither being influential enough to dominate the state as Pericles had been able. Cleon was the leader of the war group and their policies actually gave Athens some serious advantages. By the end of this period Athens was forming bases all around the Peloponessus, most notably Pylos, where the Athenians could raid and incite rebellions. The Spartans were fearing a massive Helot rebellion and the defection of their Democratic allies.

Many Athenians would become weary of war and Nicias grew an increasinly strong pressure to make peace. Finally with the death of Cleon the peace party won and Athens made a peace with Sparta. This peace was not reconized by Sparta's allies, and not followed very long between Sparta and Athens. This led to a time of relative peace, but led to the Sicilian campaign. Alcibaides did propose the campaign, but if he had his way he would have only had 60 ships, not nearly enough for disaster. Nicias, beaten on the policy, used an elegant speech to persuade his fellows the expedition would require a massive force, hoping to disuade his fellows. Instead he caused the fleet to raise to 100. The expedition would go badly(largley for Nicias blunders) and Nicias again tried his tact. He could retreat and loose honor or use cunning. He told the Athenians they must retreat or send reinforcents. Again his methods failed and the Athenians sent 70 more ships, making what originally was a small affair into a truly massive undertaking. This disaster was not Alcibaides, but much more due to Nicias.

As for Alcibaides trading sides, you must look at it in context. Before the Sicilian Expedition Alcibaides mocked some religous rite. This coinceded with the defacing of some religous statues(Alcibaides wasnt invlovled in that) and as a result the Athenians took it as treason. Instead of trying him with the army and his loyal supporters in town they waited till the expedition had left, then recalled Alcibaides to be tried in a town with no allies. He was going to be killed and so he decided instead of returning to Athens he would sail for Sparta. Who can be a patriot when their home wants them dead? Feeling betrayed Alcibaides made life in Sparta, but most were very distrusful of him. (It was alleged that an earthquake forced him out of King Agis's bedroom.). Alcibaides never really wanted to be a Spartan and with powerful enemies there is was simply not safe to do so anyways. So he went on an Ionian campaign and jumped to the Persians. We can safely assume he never planned on being Spartan for long, but simply prefered the Spartans to death as a traitor, for a crime that was hardly very treasonous.

Oh yea, and Sparta joined in the Sicilian Campaign long before Alcibaides arrived. He convinced them to help the Chois rebellion after Sicily, but they were bound to help one of the places trying to rebel, so its not like he led them to action where they would otherwise be inactive.