The Greeks loved music, and made it an important part of their lives. They thought of music as a way of honoring the gods, and making the world a more human, civilized place. Unfortunately we really have no idea what Greek music sounded like, because there were no tape recorders or anything like that then, and they had no way of writing down music either.
Apollo playing the lyre
We do know what kind of instruments the Greeks had. They had pipes, and lyres, and drums, and cymbals. Their pipes were made from wood or reeds, with holes cut in them for your fingers to play the tune. Some were played vertically, like a recorder, and some were played sideways, like a flute. Sometimes people played more than one pipe at a time. Pipes and drums were played in a loud, lively way, for dancing, and people played this music when they were worshipping Dionysos, the god of wine and parties.
The Greeks also had lyres, which are like small harps, and might have sounded something like a guitar. According to the Greek story, the first lyre was made from a turtle shell by the god Apollo when he was a baby. Apollo was the god of reason and logic, and the Greeks thought of music as a great expression of order and patterns. Lyre music was played calmer, and more soothingly, than the pipes and drums.