To edit your site after you first Publish it, just log in through weebly.com (or through the Log In button on the upper right of this page), make your changes in the editor and Publish the site again. Any changes you've made to the site will immediately appear on the live site after you press the Publish button.
Note that if you do not see the changes you've made after you Publish the site, it's probably because your browser is displaying an older version of the page from its cache. Just reload the page using your browser's reload button to bring up the newest version of your site.