The easiest thing to do is to let them type mysite.com/example/—that is, with a slash on the end. You do this by creating a folder inside your root folder called /example/ and moving the example.php file to that folder and renaming it as index.php.
An alternative is to rewrite your URLs with a .htaccess rule, but that's a little tricker and messier ... although it means you don't have to restructure your site.
Often sites have a structure like mysite.com/example because their pages are served up by a CMS that creates such URLs by default. But rebuilding your site within a CMS is most likely the most time consuming option.