Hover a module card (or a section in Live edit) to reveal the action icons:

• Edit (pencil) – open the module's options.
• Duplicate Module (clone icon) – inserts an exact copy, including all its settings, right after the original ("The module was duplicated with success").
• Move up / Move Down (chevrons) – swap the module with its neighbour.
• Delete Module (trash) – asks "Are you sure you want to delete this module? This action cannot be undone." and removes it.

All actions apply instantly to the live page; there is no separate publish step for DIY pages. Only DIY pages allow adding/moving/deleting modules – fixed templates only expose their own options.