The most common way of presenting menus is in the menu bar. This is done by putting the menus in the menu bar of an interface, typically by using :menu-bar in define-interface. It is also possible to set the menu bar dynamically using (setf interface-menu-bar-items).
On Cocoa, you may want to define the application menu, the menus that are shown when no interface is active, and maybe a Dock context menu. For these, you will need to define your own subclass of cocoa-default-application-interface, and use set-application-interface on an instance of this class. See entry for cocoa-default-application-interface.
Pane-specific menus are invoked automatically by the system for the appropriate user gesture. See Popup menus for panes for a full discussion of the mechanism that finds the menu to raise.
There is also a special pane popup-menu-button, which raises a menu when clicked.
In addition, you can raise a menu programmatically by calling display-popup-menu.
CAPI User Guide and Reference Manual (Unix version) - 3 Aug 2017