They aren't buttons. They are slots into which a Great Work can be placed. The quill and inkwell slot is for a Great Work of Writing, the artist's palette is for Great Works of Art (or for Artifacts that your archaeologists dig up), and the musical note (not displayed in your screenshot) is for Great Works of Music.
The only ways to acquire Great Works is to (1) generate them by "bulbing" relevant Great Persons (Great Writers, Great Artists, Great Musicians -- collectively GWAMs), (2) acquire them from the AI by conquest, or (3) in the case of the Parthenon, just build the Partheon (comes with a free great work of art).
You can generate GWAMs in a manner similar to other Great Persons: (A) build the relevant guilds and work those specialist slots, (B) select a GWAM as your free Great Person from, e.g., the Liberty finisher, the Leaning Tower of Pisa or the Mayan Long-Count, (C) build a wonder that comes with a GWAM (e.g., Broadway comes with a Great Musician), (D) select the social policy that provides one Great Artist, or (E) if you have the right social policies or religious beliefs, buy GWAMs with faith starting in the Industrial Era.