Monotonic music mainly, with lyre, drum, trumpet and flute, with different "modes" to evoke different states of mind. The ancient Greeks considered their music and lyrics to be central to who they were as a civilization, and, of course, to be a gift from the gods. As best I can tell, poetry (the lyrics) was never offered without accompanying music.
The group Melpomen recreates the ancient sounds from surviving fragments. (Samples of the music at the Amazon site.)
Wiki has a fine summary of ancient Greek music. Interesting to read that Plato (c 400 BC) complained about the modern music which defied old forms.
Image: Music lesson, c.460 BC, from this site about ancient Greek music.