Trouble Understanding jQuery-UI Popup Menu

I'm trying to figure out how to make a pop-up menu using the jQuery UI menu widget.

After searching around, I finally found the following demo that does what I want:

http://view.jqueryui.com/menubar/demos/popup/popup-menu.html

However, I am having a little trouble understanding this demo. For example:

1. What is making the menu hidden before any of the buttons are clicked?
2. What is causing the menu to close when it's open and I click somewhere else on the page?

Any help appreciated.

I believe this may be what you're looking for. When you call .menu(), lots of things are triggered in the _create() function (as Derek said), like setting class names etc. Then, at lines 123-135 in jquery.ui.menu.js, this happens:

    this.refresh();

    // Clicks outside of a menu collapse any open menus
    this._on( this.document, {
        click: function( event ) {
            if ( !$( event.target ).closest( ".ui-menu" ).length ) {
                this.collapseAll( event );
            }

            // Reset the mouseHandled flag
            mouseHandled = false;
        }
    });

The second part makes sure all menus are collapsed when the user clicks on the page (this.document) outside a menu (.ui-menu): this.collapseAll() is called, which calls this._close(), which in turn calls hide(). This should answer your second question.

As for your first question, The first thing the refresh() function does is:

    // Initialize nested menus
    var menus,
        icon = this.options.icons.submenu,
        submenus = this.element.find( this.options.menus + ":not(.ui-menu)" )
            .addClass( "ui-menu ui-widget ui-widget-content ui-corner-all" )
            .hide()
            .attr({
                role: this.options.role,
                "aria-hidden": "true",
                "aria-expanded": "false"
            });

This finds all submenus not previously initialized (in this case all of them since we're coming from _create()) and initializes them, which includes hiding them.