How is he killed? Arya uses a face from the Hall of Faces to transform herself into another person. (It's actually the face of the girl who she assists in killing by the fountain in the House of Black and White.) She gains an audience with the twisted Ser Meryn (who, you may recall, is on her list) by posing as a young prostitute, and once she's alone with him, she dons her own face again and stabs him repeatedly in the eyes. She slits his throat once she's sure he knows who she is and why she's killing him.
Is he definitely dead? Yes.
Level of devastation: Negative ten. This guy is the worst.