In AdminCP, you can create a new option link on the left pane and call your own php file and use existing vB functions and includes. You do this by creating an xml file in /core/includes/xml folder. As for the format in the xml, you can take a look at the existing xml files there.
As for new pages on the frontend, you do it using Sitebuilder > New Page as Lynne mentioned. You can drag and drop any module there including PHP module where you can call the vB API and your own custom functions. You can also use Ad modules and still be able to call the vB API and your own API using vB template syntax.
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