The shift cipher is named after Julius Caesar, who — his biographer Suetonius reports — used a shift of 3 in private correspondence: A became D, B became E. His successor Augustus preferred a mild shift of 1, writing simply the next letter of the alphabet. For the Roman world this was adequate protection: many of the recipients' enemies could not read Latin at all, and literate Romans did not treat letter substitution as serious cryptography anyway.
Suetonius describes both schemes plainly in The Lives of the Twelve Caesars, which is how we still know the details today. The cipher was never a state secret — it circulated as a curiosity, a neat trick of the great commander, and medieval manuscripts copied rotation tables for "Caesar's alphabet" long after the empire was gone.
Around the 9th century, in Baghdad, Al-Kindi wrote a treatise on decrypting messages: count the letters, compare the counts with the known letter frequencies of the language, and the substitution reveals itself. That single idea broke every monoalphabetic cipher at once — Caesar's included — and pushed cryptographers towards ciphers that hide letter frequencies.
The Caesar cipher survives as the textbook first cipher. Twenty-five keys are useless for real secrets, but the scheme is perfect for learning what a key is, what brute force costs, and why frequency analysis changed the field. The Renaissance answer — several alphabets in turn — is the Vigenère cipher, and this site covers it in the same way.