Overview of Mozilla embedding APIs
implemented interfaces: nsiwebbrowser nsiwebnavigation nsiwebbrowsersetup nsiwebbrowserpersist nsiwebbrowserfind nsiwebbrowserprint nsiwebbrowserfocus nsibasewindow requestor interfaces: nsidomwindow nsidomdocument nsiwebprogress nsiclipboardcommands nsiprompt related interfaces: nsiprompt nsiwebbrowserchrome nsiwebbrowsersitewindow nsiwebprogresslistener nsicontextmenulistener nsiprintoptions overview: most of gecko's functionality is exposed through the nswebbrowser component.
...context menu notifications right-click context menu notifications are passed up to the embedding application through the nsicontextmenulistener interface.

Embedding Tips
make your chrome object implement the nsicontextmenulistener or nsicontextmenulistener2.
... the nsicontextmenulistener::onshowcontextmenu() method will be called with the dom node that the context applies, the dom event plus some flag combinations that assist in determining what menu to display (document, link, image, selected text etc.) how do i implement tool tips?

nsIWebBrowser
the chrome may optionally implement nsiinterfacerequestor, nsiwebbrowserchromefocus, nsicontextmenulistener and nsitooltiplistener to receive additional notifications from the browser object.
... see also nsibasewindow nsicontextmenulistener nsidomwindow nsiembeddingsitewindow nsiinterfacerequestor nsishistorylistener nsitooltiplistener nsiuricontentlistener nsiweakreference nsiwebbrowserchrome nsiwebbrowserchromefocus nsiwebprogresslistener ...