In the Battle of Thermopylae, the Spartan army along with an alliance of Greek states took on the massive Persian force at the pass of Thermopylae. In one of the most famous last-stands in history, the Spartans and Greeks held of the Persian army for several days, funneling them through the pass or sometimes referred to as the "Hot Gates". King Leonidas, commander of the spartans, set up his men in the pass and used their phalanx tactic. The combination of both these strategies made the Persians numbers count for nothing. It is believed that after two and a half days of battle, Ephilates, a local Spartan citizen betrayed Leonidas by leading the Persians on a goat path which took them directly to the top of the pass.

The earliest example of the phalanx formation is thought to be the ancient Egyptians. Judging by the Egyptian's historic records, they were the first people to use this rectangular formation in battle. It is still unclear if there is a connection between the Greek and Egyptian's phalanx. The phalanx is a formation in which soldiers would line up very close together. They would lock shields and project their spears out over the top of the human wall. The soldiers would then run and crash into the enemy forces with their shields. While the enemies were off-balance, the soldiers thrust into their enemies with their spears. After they had taken out the first wave of attackers, they would repeat the strategy multiple times untill the phalanx was broken up by enemy forces. It is thought that Sparta's military was so powerful mainly because of this battle technique. Here is a video from the movie 300, that demonstrates how the phalanx works. Phalanx Demonstration

There are many other resources that take very in-depth looks into the Spartan army. Here are links to a few of them:

The Spartans: The World of the Warrior-Heroes of Ancient Greece
Gates of Fire: An Epic Novel of the Battle of Thermopylae
The Peloponnesian War: Athens, Sparta, and the Struggle for Greece
Last Stand of the 300 DVD
Agoge - Spartan Military Training
History of Sparta
Best Books on Ancient Sparta
War and Valor
Map of Sparta
300