It's kind of in 2 parts - the relevant ascx(s) inherit from portalmodulebase , which is our base object for portal functionality. Within that you can see a check for the necessary permissions, and code such as

_actions.Add(GetNextActionID, Localization.GetString(ModuleActionType.DeleteModule, Localization.GlobalResourceFile), ModuleActionType.DeleteModule, ModuleConfiguration.ModuleID.ToString,

"action_delete.gif", "", "confirm('" + DotNetNuke.UI.Utilities.ClientAPI.GetSafeJSString(Localization.GetString("DeleteModule.Confirm")) + "')", False, SecurityAccessLevel.Admin, True, False)

This is picked up in \Library\Components\Skins\ActionBase.vb

However, this code only marks the module as being sent to the recycle bin (i.e. a "soft" delete). The actual code to delete a module looks like this:

\Website\admin\Tabs\RecycleBin.ascx.vb

you can either use the code I showed in the first snippet or else (more conventionally) add it as part of the ascx.vb/ascx.cs i.e. if you page is called "mypage" , then alter it's class definition to inherit from portalmodulebase (so it can leverage dotnetnuke security, positioning etc.) and implments the optional IActionable interface - this will allow you to add custom actions , the parser will automatically look for a ModuleActions property e.g.

Partial Class MypageInherits Entities.Modules.PortalModuleBaseImplements Entities.Modules.IActionable