The ancient Greeks told the story of their sexuality through paintings, legends, myths, theater, and sculpture.
For example, the satyr plays of ancient Greece correspond to the sex or romantic comedies of today. These plays featured half-man, half-goat characters who spouted ribald lines, donned phalluses, engaged in sexual trysts, and imbibed wine to excess. Few manuscripts of ancient Greek satyr plays survived intact, but Euripides's Cyclops did. Meanwhile, the Iliad was one play that celebrated heterosexual love (the one between Achilles and the beautiful Briseis). In the play, Achilles was so furious with Agamemnon for taking Briseis from him that he refused to fight against the Trojan forces. You can see a painting of Patroclus separating Briseis from Achilles here.
In the area of sculpture, the Greeks could not have been more adventurous. Sexually-explicit sculptures were de riguer, and the Greeks were certainly not bashful about their sexual proclivities. One such sculpture evidenced a homage to bestiality and involved the god Pan making love to a goat. Vases of the time showed satyrs in the midst of sexual ecstasies and other satyrs assuming self-pleasuring stances. Certainly, Greek erotic art was not for the faint of heart.
Greeks also did not shy away from portraying pederasty in their art. Historians bear witness to drinking cups featuring erotic scenes between men and younger males. Greek legends tell of the Greek god, Zeus, who raped the handsome Ganymede. Incidentally, Ganymede is also sometimes known as the Greek god of homosexual love. You can read more about Ganymede here.
As we can see from the above examples, ancient Greeks left behind many examples of their sexuality in their art. For more information, please refer to the links below.