PMroz has the right idea though some pages may require logging in or use background requests (AJAX) to pull in data after you navigate to the page.
For those, it's better to use File > Internet Open and change Open As: to Web page. After that, you can login/click hyperlinks, etc and use File > Import Table As Data Table... when you reach the data. From there, you can click through more links like Next | Prev etc on the page and keep importing as needed.
Of course, this is impractical for lots of pages so JSL is the way to go there as PMroz says (assuming you're not stymied with a login page).