This shows the first and second verses of the First Delphic Hymn to Apollo, carved in marble for the Athenian Pythaides festival in 128 BC in Delphi. The composer’s name is Athenaios Athenaiou (Athenaios, son of Athenaios).
The melody is written above the lyrics, and shows which notes to sing (according to the Greater Perfect System).
The rhythm is inherent in the poetics of the verse. For example, we see cretics (instead of, say, iambs or dactyls) so we know the time signature is 5/8.
Here is a performance of the hymn.