When I took ancient history in middle school, my teacher had a clearly very old textbook she used for the greek unit, and it went into great detail about how ancient spartan kids were raised, and the details of how athenian democracy worked. however, there was recently some controversy over how it might not necessarily have been accurate, so i was wondering how we know what we know.
Much of what we know comes from non-Spartan greeks living contemporaneously with the Spartans. For the period of the Peloponnesian War we have Thucydides, for the period of Spartan dominance over Greece following their victory over Athens we have Xenophon, and for the period covering their decline and fall we have Polybius.
Most of this, though, is narrating the history of wars and politics, so they mention Spartan daily life only incidentally. Thankfully, Xenophon was a pro-Spartan Athenian (c. 430 – 354 BC), and his Hellenica: A History of My Times gives a lot of information about the end of Sparta's epic struggle with Athens and the rise of Sparta to preeminence in Greece, and he even wrote a separate biography of the Spartan king Agesilaus, who was a close personal friend of his.
Perhaps most important to our understanding of their society is a work called The Constitution of Sparta which is short, but gives lots of details about their laws, customs, child raising techniques, and general way of life. It's historically attributed to Xenophon, but many scholars now think it was written by someone else living at the same time as Xenophon.
Finally, Plutarch (c. AD 46 – AD 120) wrote biographical lives of several Spartans spanning their whole history which relied on sources now lost to us, and they also give vital insight into Spartan lifestyle. He also compiled a compendium of Spartan sayings that are very interesting to read.