There’s nothing you need to do to publish your website. Every time you make a change within your Control Panel and click the SAVE button (see image below), the changes are automatically published to your live website.
If you are searching Google and are wondering why your website is not listed there, it is because you first need to add your site to the search engines. Please follow our tutorial here - http://www.iconosites.com/blog/2011/12/how-to-add-your-website-to-search-engines-iconosites-website-builder/
Then, it still may take several weeks before your website shows up in the search engines (this is entirely up to them).