There are a lot of different conflicts/plot threads/going on here, and though we don't want to mix our metaphors, let's just say they all come to…a head.
One night in Herod's palace, we find a group of soldiers watching the Tetrarch banqueting; one of the soldiers, a young Syrian, is particularly taken with Salomé. We learn, too, that Jokanaan, a prophet, is being held captive in a cistern. When the prophet cries out, the soldiers begin discussing his authority and religion in general.
Salomé, disgusted by the way her stepfather looks at her, comes up to the terrace where the soldiers are watching. When she hears Jokanaan crying out, she starts asking questions about him and convinces the young Syrian to her see the prophet. A tense confrontation ensues: Salomé lusts after Jokanaan, but Jokanaan hates her; she praises him and insults him before deciding, once and for all, that she will kiss him.
Horrified by the confrontation, the young Syrian kills himself. Soon after, Herod appears with his entourage. He's still keen on seeing (or, rather, staring at) Salomé. The presence of the dead body really dampens the mood, though. Furthermore, the move upstairs puts Herodias in hearing range of Jokanaan, who hurls insults at her.
After listening to the Jews and Nazarenes argue about Jokanaan—you see, the Jews really would like deal with the prophet themselves—Herod decides he'd like to see Salomé dance. Salomé has no interest in seeing her stepfather, let alone dancing for him. Herod promises to give her anything she wants, up to half his kingdom.
Salomé refuses to dance. Herodias supports her decision. Herod insults Herodias. Finally, Salomé seems to come around. She gets Herod to swear to do whatever she asks. He swears. Herodias continues to object; she's still put off by Jokanaan.
Salomé performs the (sexy) Dance of the Seven Veils. She then asks for Jokanaan's head on a silver platter. Herodias is delighted. Herod is horrified. He tries to get Salomé to change her mind, but she won't budge. He calls for Jokanaan to be beheaded.
Salomé is given Jokanaan's head. She addresses him/it, getting mad at him for rejecting her. Still, she tells him, she thinks he's hot. Herod is disgusted. Herodias is pleased. When the stage goes dark, Salomé kisses Jokanaan. Herod, disgusted, orders Salomé to be put to death. The soldiers crush her beneath their shields.